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Chen, Han-Mei (2014) Physical model tests and numerical simulation for assessing the stability of tunnels. PhD thesis, University of Nottingham.
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Physical Model Tests and Numerical
Simulation for Assessing the
Stability of Tunnels
Han-Mei Chen
Thesis submitted to The University of Nottingham
For the degree of Doctor of Philosophy
July 2014
This thesis is dedicated to
my grandma, my parents and my husband.
i
ABSTRACT
Nowadays, numerical modelling is increasingly used to assess the stability of tunnels
and underground caverns. However, an analysis of the mechanical behaviour of
existing brick-lined tunnels remains challenging due to the complex material
components.
One promising approach is to carry out a series of small-scale physical tunnel model
tests representing the true behaviour of a prototype under extreme loading in order to
validate and develop the corresponding numerical models. A physical model test is
advisable before any field study, which might be dangerous and costly. During the
tests, advanced monitoring techniques such as the laser scanning and
photogrammetry would be used to register tunnel deformation and lining defects.
This investigation will show how these may substitute or supplement the
conventional manual procedures.
Simultaneously, numerical models will be developed, primarily using FLAC and
UDEC software, to simulate the physical models after comparing their results. In this
way, numerical simulations of physical models would be achieved and verified.
These numerical models could then be applied to the field study in the future
research, enabling accurate prediction of the actual mechanical behaviour of a
masonry tunnel, in combination with advanced monitoring techniques.
ii
ACKNOWLEDGEMENTS
Firstly, I am heartily grateful to my supervisor Prof. Hai-Sui Yu and Dr. Martin
Smith who continuously support and encourage me throughout this research project.
I am greatly indebted to them whose guidance was invaluable to me.
I would also like to cherish the memory of my supervisor Dr. David Reddish who
passed away for his academic guidance and care. Without him, I would not be able
to enjoy my work as I am. I would also like to express my gratitude to the senior
experimental officer Dr. Nikolaos Kokkas and the former research fellow Dr. Philip
Rowsell for their advice and assistance on my research.
I am thankful to all technicians working in the Nottingham Centre for Geomechanics
and the laboratory of Civil Engineering for providing their assistance throughout the
experimental work.
Finally, my sincere thanks go to my family members and friends who always
supporting me during the PhD course in The University of Nottingham, UK.
iii
TABLE OF CONTENTS
ABSTRACT ............................................................................................................. i
ACKNOWLEDGEMENTS ................................................................................... ii
TABLE OF CONTENTS ..................................................................................... iii
Chapter 1 INTRODUCTION ............................................................................ 1
1.1 Challenges ...................................................................................................... 1
1.2 Aim ................................................................................................................. 2
1.2.1 Objectives ................................................................................................ 2
1.2.2 Methodology ............................................................................................ 2
1.3 Structure of the thesis ..................................................................................... 3
Chapter 2 LITERATURE REVIEW ................................................................ 5
2.1 Introduction .................................................................................................... 5
2.2 Stability concerns of tunnels .......................................................................... 5
2.2.1 Terminology in tunnelling ....................................................................... 5
2.2.2 Permanent linings ................................................................................... 6
2.2.3 Hazards ................................................................................................. 11
2.2.4 Regular inspection ................................................................................ 22
2.2.5 Maintenance .......................................................................................... 23
2.2.6 Summary ................................................................................................ 24
2.3 Tunnel monitoring methods ......................................................................... 25
2.3.1 General introduction ............................................................................. 25
iv
2.3.2 Monitoring tunnel distortions and convergence ................................... 25
2.3.3 Identifying damaged defects on tunnel shells........................................ 30
2.3.4 Final discussion .................................................................................... 44
2.4 Masonry structure review ............................................................................. 44
2.4.1 Introduction to masonry structures ....................................................... 44
2.4.2 Brick bond patterns ............................................................................... 45
2.4.3 Brick/Mortar/Brickwork properties ...................................................... 49
2.5 Numerical modelling review ........................................................................ 58
2.5.1 Introduction to numerical simulation strategies ................................... 58
2.5.2 Numerical analysis of masonry structures ............................................ 59
2.6 Chapter summary ......................................................................................... 64
Chapter 3 PHYSICAL MODEL TESTS ........................................................ 65
3.1 Introduction .................................................................................................. 65
3.2 Design of physical model tests ..................................................................... 66
3.2.1 Mortar mix proportion .......................................................................... 66
3.2.2 Loading style ......................................................................................... 67
3.2.3 Test variations ....................................................................................... 67
3.3 Design of a physical model .......................................................................... 68
3.3.1 General introduction ............................................................................. 68
3.3.2 Brick bond pattern................................................................................. 69
3.3.3 Rigid box ............................................................................................... 69
v
3.4 Physical model materials.............................................................................. 70
3.4.1 Brick ...................................................................................................... 70
3.4.2 Mortar ................................................................................................... 71
3.4.3 Surrounding soil .................................................................................... 72
3.5 Model construction and loading process ...................................................... 73
3.5.1 Construction of brickwork liner ............................................................ 74
3.5.2 Rigid box ............................................................................................... 76
3.5.3 Plastic sheeting ..................................................................................... 78
3.5.4 Surrounding soil .................................................................................... 78
3.5.5 Loading system installation .................................................................. 79
3.5.6 Loading procedures .............................................................................. 81
3.6 Tunnel monitoring instrumentation ............................................................. 82
3.6.1 Advanced monitoring techniques .......................................................... 82
3.6.2 Potentiometer ........................................................................................ 85
3.7 Test results of the first and the second models under uniform load............. 86
3.7.1 Ultimate load capacity and tunnel mode of failure ............................... 86
3.7.2 Deflection behaviour ............................................................................. 88
3.7.3 Cracking behaviour ............................................................................... 91
3.8 Test results of the third model under concentrated load .............................. 92
3.8.1 Ultimate capacity and tunnel mode of failure ....................................... 92
3.8.2 Deflection behaviour ............................................................................. 95
vi
3.8.3 Cracking behaviour ............................................................................... 97
3.9 Post-processing work of advanced monitoring techniques .......................... 98
3.9.1 General introduction ............................................................................. 98
3.9.2 Tunnel monitoring and data processing of measurements using
photogrammetry .................................................................................................. 98
3.9.3 Tunnel monitoring and data processing of measurements using the
Laser Scanning Technique ................................................................................ 103
3.9.4 Results and comparison of the monitoring equipment ........................ 106
3.10 Summary .................................................................................................... 118
3.10.1 Design of different physical models .................................................... 118
3.10.2 Programme of physical model testing ................................................. 118
3.10.3 Monitoring techniques ........................................................................ 119
Chapter 4 NUMERICAL SIMULATION .................................................... 121
4.1 General introduction................................................................................... 121
4.2 Programme of material testing ................................................................... 121
4.2.1 General introduction ........................................................................... 121
4.2.2 Brick .................................................................................................... 122
4.2.3 Mortar ................................................................................................. 128
4.2.4 Surrounding soil .................................................................................. 129
4.2.5 Brickwork (Triplet / Couplet) .............................................................. 133
4.3 Modelling issues of brick-lined tunnels ..................................................... 143
vii
4.3.1 Modelling approaches ......................................................................... 143
4.4 Introduction to FLAC ................................................................................. 144
4.4.1 General introduction ........................................................................... 144
4.4.2 Fields of application ........................................................................... 145
4.4.3 Comparison with the Finite Element Method ..................................... 146
4.4.4 General solution procedure ................................................................ 148
4.4.5 Further developments.......................................................................... 150
4.5 Numerical modelling of physical models using FLAC .............................. 150
4.5.1 Materials and interface properties...................................................... 150
4.5.2 Model generation ................................................................................ 152
4.5.3 Parametric study ................................................................................. 153
4.5.4 Results analysis of the parametric study ............................................. 173
4.5.5 Modelling results ................................................................................. 175
4.6 Introduction to UDEC ................................................................................ 178
4.6.1 General introduction ........................................................................... 178
4.6.2 Fields of application ........................................................................... 179
4.6.3 Comparison with other methods ......................................................... 180
4.6.4 General solution procedure ................................................................ 181
4.6.5 Further developments.......................................................................... 183
4.7 Numerical modelling of physical models using UDEC ............................. 183
4.7.1 Materials and interface properties...................................................... 183
viii
4.7.2 Model generation ................................................................................ 185
4.7.3 Parametric study ................................................................................. 186
4.7.4 Results analysis of the parametric study ............................................. 193
4.7.5 Modelling results ................................................................................. 195
4.8 Discussion .................................................................................................. 200
4.8.1 Comparison with physical model tests ................................................ 200
4.8.2 Comments ............................................................................................ 202
4.9 Prediction of numerical simulations........................................................... 203
4.9.1 Introduction ......................................................................................... 203
4.9.2 Overburden soil depth ......................................................................... 204
4.9.3 Concentrated load ............................................................................... 206
4.10 Chapter summary ....................................................................................... 208
4.10.1 Programme of material testing ........................................................... 208
4.10.2 FLAC and UDEC models .................................................................... 208
4.10.3 Prediction of numerical modelling...................................................... 208
Chapter 5 CONCLUSIONS AND RECOMMENDATIONS ..................... 209
5.1 Conclusions ................................................................................................ 209
5.2 Recommendations for future research ....................................................... 213
REFERENCE ..................................................................................................... 215
PICTURES AND TECHNIQUE SHEET REFERENCE .............................. 221
APPENDIX A: LABORATORY TEST RESULTS ........................................ 222
ix
APPENDIX B: POST-PROCESSING WORK OF MONITORING ............ 231
APPENDIX C: NUMERICAL MODELLING RESULTS OF
PREDICTION .................................................................................................... 239
1
CHAPTER 1 INTRODUCTION
1.1 Challenges
Most railway tunnels made of brickworks in UK were built decades ago; some are
even over a hundred years old. They are subjected to degradation such as spalling,
perished mortar and loose bricks during their service life. Tunnels can also be
subjected to ground stresses, which could cause severe deformation and damage to
the tunnel brickwork support. Degradation and tunnel deformation are major threats
to the tunnel’s durability and can lead to a collapse if not controlled. It is noted that
this project is concentrated on the study of railway tunnels, especially their
brickwork supports.
Therefore, it is important that the stability and deterioration of these tunnels be
assessed by regular/frequent monitoring work. There are also benefits (such as cost,
life expectancy and so on) by building numerical models to analyse and predict the
mechanical behaviour of long-term tunnels before serious problems occur.
Tunnel monitoring has predominantly been a manual procedure, which is time-
consuming and subjective, giving rise to variance in the standards and quality of
examination.
Although several numerical modelling approaches to old tunnel masonry structures
have been proposed (Idris, 2008 and 2009), the modelling and the mechanical
behaviour analysis of existing brick-lined tunnels remain challenging due to the
complex material components.
2
1.2 Aim
The overall aim of the PhD research is to assess the stability of brick-lined tunnels
through physical and numerical modelling.
1.2.1 Objectives
1) Review of existing problems with brick-lined tunnels and methods for
maintaining and monitoring the condition of the tunnels;
2) Investigate the stability of small-scale physical models of brick-lined tunnels.
Advanced monitoring techniques will be used to investigate;
3) Investigate the use of numerical modelling of brick-lined tunnels;
4) Assess, analyse and evaluate physical modelling and numerical simulation;
5) Assess the stability of brick-lined tunnels through the two approaches used.
1.2.2 Methodology
The methodology adopted for the project is as follows:
1) Literature review is undertaken to develop understanding and background
knowledge (Objective 1);
2) Laboratory trials are designed, experiments performed are to fulfill objective 2;
3) Numerical simulation using FLAC and UDEC performed is to match the
physical lab trials (Objective 3);
4) Advanced monitoring techniques are used to compare with traditional
approaches;
5) Results from 2), 3) and 4) are produced and analysed, comparisons are made;
6) Conclusion are drawn.
3
This can be explained by Figure 1.1.
It is noted that these physical model tests are not required to replicate the real tunnels
with various conditions, but should provide similar boundary and loading conditions,
which are easily measured and assessable.
Figure 1.1 The methodology of the overall research
1.3 Structure of the thesis
The thesis consists of five chapters.
Chapter 1 introduces the current problems associated with tunnel stability. The main
objectives and an outline of the report are also presented.
Chapter 2 reviews tunnel stability concerns, including tunnel instability phenomena
and their causes, permanent linings as structure support and maintenance, etc. In
addition, different existing monitoring methods have been proposed, followed by an
outline of various numerical simulation approaches and their characteristics as well
as brickwork properties. The modelling of tunnel masonry structures, multi-ring
masonry arch bridges and masonry building structures has also been reviewed.
4
Chapter 3 reports a series of small-scale physical tunnel models which have been
designed, prepared and tested, including the post-processing and analysis of
monitoring equipment, as well as the loading process of the physical models.
Chapter 4 demonstrates the modelling of the physical model, by both FLAC and
UDEC software, for the application of the finite difference method and distinct
element method respectively. The accuracy of the numerical models using these two
methods has been verified by the physical model results produced and reported in
Chapter 3 as part of the research, A comprehensive parametric analysis is used to
identify the influence of both stiffness and strength parameters in the relevant
numerical procedures. Initially, a programme of material testing in the laboratory has
been conducted as a reference to the numerical modelling.
Chapter 5 draws the conclusions of the work and proposes potential future research
directions in both physical model tests and numerical simulations.
5
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction
This literature reviews tunnel stability concerns, existing problems with brick-lined
tunnels and methods for maintaining and monitoring the condition of the tunnels.
Furthermore, tunnel masonry structures and their properties have been reviewed,
followed by an outline of various numerical simulation approaches, as well as the
numerical modelling of tunnel masonry structures, multi-ring masonry arch bridges
and masonry building structures.
2.2 Stability concerns of tunnels
2.2.1 Terminology in tunnelling
The various locations on the tunnel cross-section are denoted by the indicated names,
as Figure 2.1 shows.
Figure 2.1 Parts of a tunnel cross-section (Kolymbas, 2005)
Other terms defined below are also useful in this research.
Transverse direction: in the horizontal plane, normal to the axis of the tunnel.
Crown
Side
Lining
Bench
Invert
6
Longitudinal direction: in the direction of the tunnel axis.
Profile: the shape of a tunnel cross section, such as circular, rectangular, mouth or
horseshoe.
Tunnel heading: the workface at the front of the tunnel where soil excavation is
being made (NG et al., 2004).
2.2.2 Permanent linings
1) Introduction
Linings (permanent) are always expected in soft ground tunnels and are often used in
rock tunnelling. They play a crucial role in the stability of tunnels and are
constructed for several reasons (Megaw et al., 1981):
a) To provide sufficient structural support
b) To eliminate or reduce water ingress or seepage
c) To provide an internal surface and accommodate the operational tunnel profile
2) Structural support
After the excavation of a tunnel, the initial stable equilibrium of the ground is
disturbed and stress redistribution starts to take place. With the addition of support
structures, a new stress pattern will be set up.
The need for support depends on the actual conditions. In soft, plastic ground, the
development of hydrostatic pressure makes it essential to build up support to carry
the whole overburden pressure. In homogeneous rock, structural support seems to be
unnecessary; an arching action of stress will develop efficiently to support the tunnel.
7
The timing of the support construction is critical to restrain any deformation that
may cause collapse. It is largely judged by working experience associated with the
ground properties. The stress redistribution after support construction would
establish a new and stable equilibrium.
3) Operational tunnel profile
The shape of a tunnel profile usually depends on the ground conditions and the
operational function of the tunnel.
An arch is ideal to support pressure and is widely used for the tunnel roof. The
tunnel profile might be completed with vertical sidewalls to form a horseshoe, a
whole circle or an ellipse.
The horse-shoe cross section often appears in railways. In these tunnels, the
development of lateral stress requires a lining to carry loads. The sidewalls need to
be anchored at the toe, where the stresses are largely concentrated.
The structural advantage of the circular form is the ability to endure loads from all
directions in the ground. Thus, this form is usually adopted for the carrying of water
or sewage, excavated by a shield machine or a full-face machine. Other forms, such
as rectangular design are normally used in highway tunnels.
4) Principal materials for permanent lining
For bored tunnel linings, the principal materials are (Megaw et al.,1981):
a) Concrete
o In situ concrete
8
o Sprayed concrete
o Segmental rings of precast concrete
b) Cast-iron and steel
o Segmental rings of bolted cast-iron
o Segmental linings of welded steel
c) Brickwork and masonry
In situ concrete
Concrete placed in situ is designed to accommodate any shape of cross section on an
extensive scale. It is also ideal for the filling of the overbreak after excavation and
unbounded voids between the lining and the raw tunnel surface. Using a travelling
shutter behind the working face, concrete is cast in time for tunnel support.
Sprayed concrete
Combined with rock bolts, steel arches or mesh reinforcement, sprayed concrete is
widely utilised nowadays. It plays an essential role in the New Austrian Tunnelling
Method (NATM), whose principle is to control the development of stresses and
deflections as well as their interaction with lining supports.
Segmental rings of precast concrete
All circular segmental rings provide an immediate supporting structure of great
strength and useful flexibility. The principal design and dimensions of cast-iron and
precast concrete segments are similar. Compared with cast-iron segments, the cost of
materials and fabrication of precast concrete segments is much less. Furthermore, the
superior rigidity of precast concrete segments enables them to endure damage during
9
handling and jacking as well as after erection. Therefore, precast concrete segments
have become the first major substitute for segmental linings of cast-iron.
Segmental rings of bolted cast-iron
The circular shape is mostly used for cast-iron segments, whereas an ellipse form is
sometimes adopted in sewers. Cast-iron has adequate compressive strength but
relatively low tensile strength and is brittle. When used in circular tunnel rings, most
of the ground loadings are direct compressive stresses with few tensile stresses and
bending moments.
Segmental linings of cast-iron seem to perform better in terms of water tightness and
operational convenience than those of precast concrete.
Segmental linings of welded steel
Steel material is not widely used in the world of segmental linings. Because of the
extra strength in tension and bending, it is sometimes utilised in cases of abnormal
loadings imposed by adjacent structures etc. The corrosion resistances in the ground
for steel and cast-iron are similar.
Brickwork and masonry
Neither brickwork nor masonry is still employed as the structural lining material of a
tunnel today. This is in contrast to the early railway age, around the nineteenth
century, when most British railway tunnels were built with bricks that had often been
manufactured on site. The term ‘English method’ refers to alternating excavation and
timbering with bricklaying in brick-lined tunnel construction.
10
Figure 2.2 Diagram of the tunnelling shield used to construct the Thames
Tunnel (Wikipedia, 2013)
In 1818, Sir Marc Isambard Brunel patented a tunnelling shield inspired by the
shipworm. Workers worked in separate compartments of a reinforced shield of cast
iron, digging at the tunnel-face. Periodically, the shield could be driven forward by
large jacks and the opened tunnel surface behind it could be covered with cast iron
lining rings (see Figure 2.2).
Brunel's invention provided the basis for subsequent tunnelling shields and it was
used to build his greatest achievement ‘the Thames Tunnel’, completed in 1842 and
remaining in use today as part of the London Underground System.
As the shield moved forward, bricklayers followed and lined the walls. The tunnel
required over 7,500,000 bricks. (Wikipedia, 2013)
For most existing tunnels, such as railway and sewer tunnels more than 100 years old,
maintenance is the most important issue. The repair of these linings may range from
11
re-pointing, local replacement of bricks to reconstruction that is more expensive
(Megaw, 1981).
2.2.3 Hazards
1) General introduction
Tatiya (2005) defined the term ‘Hazard’ as danger, risk. It is the potential to cause
losses/harm to man, machine, equipment, property assets or the environment, or a
combination of these.
Figure 2.3 shows the classification of hazards, whereby hazards are divided into two
groups: natural and man-made.
Excavation and underground operations are full of hazards as they are fighting
against nature. Hazards could easily turn into disasters with massive injuries,
fatalities and significant loss of possessions. Efforts can be made to minimise or
even eliminate some of them (Tatiya, 2005).
12
Figure 2.3 Classification of hazards (Tatiya, 2005)
2) Instability
Figure 2.4 The collapse of Duckmanton Tunnel (1959) (Courtesy of Network
Rail Ltd.)
Man-made
Chemical, mechanical &
physical
Electrical
Health hazards of industrial
substances
Chemical reaction hazards
Explosion hazards of
process materials
Flammability, fires and
explosions
Corrosion
Hardware hazards
Natural
Floods
Droughts
Fires
Earthquakes
Volcanoes
Epidemics
Wind storms
Landslides
Hazard
13
One of the biggest hazards in tunnels is the instability phenomenon. It consists of
five primary categories: tunnel collapses (as seen in Figure 2.4), disorders,
convergences, differential settlements and floods (Idris et al., 2008).
3) Tunnel ageing phenomenon
As time goes by, physical, chemical and biological processes develop inside the
masonry structure of the tunnel, which may lead to a series of instability problems
and tunnel hazards.
4) Disorder
As one of the five primary categories of tunnel instability phenomena (Idris et al.,
2008), disorder refers to deterioration and damage in tunnels, which is proved to be
strictly correlated with the ageing phenomenon. It includes longitudinal or transverse
structural cracks, convergence and partial masonry collapse. Some common disorder
phenomena in brick-lined tunnels are shown here:
14
Lining distortions
Figure 2.5 A typical tunnel deformation (Courtesy of Geodetic System Ltd.)
A typical distortion of lining can be seen in Figure 2.5.
Linings, subject to large external loads in different positions, can lead to various
deformations, with compression and tension experienced at certain sections (see
Figure 2.6).
15
Figure 2.6 Types of lining deformation (Courtesy of Network Rail Ltd.)
Spalling of the surface
Spalling means the breaking away of fragments from the surface of a wall (Lenczner,
1972). It usually happens in brickwork tunnels and results from the action of
sulphurous fumes and water on the jointing material (see Figure 2.7). In such linings,
with a large number of mortar joints and bricks from different batches, it is
16
impossible to ensure a uniform quality of all bricks and mortars. Therefore, spalling
is often local and brings about some patchy areas after maintenance.
Figure 2.7 The phenomenon of spalling (Courtesy of Network Rail Ltd.)
Ring separation
The term ‘Ring separation’ is the phenomenon when patched repairs in outer layers
of bricks subsequently fail when tunnels move and deform. Most tunnels in the UK
were built a long time ago. Their linings (made of brickwork in the past) have been
subject to years of patch repairs. In many cases, the lining part is not in close contact
with the main body of a tunnel. Thus, ring separation is likely to occur as shown in
Figure 2.8.
17
Figure 2.8 The phenomenon of ring separation (Courtesy of Network Rail Ltd.)
Open joints and the loosening of bricks
Figure 2.9 Open joints and weathered mortar (Courtesy of Network Rail Ltd.)
This is caused by the loss of mortar in two extreme ways. Dry conditions or
weathering could transform the mortar into powder which then falls out; excessively
damp conditions might wash the mortar out (see Figure 2.9).
18
Cracking
Figure 2.10 Cracks between bricks and mortars (Courtesy of Network Rail Ltd.)
Cracks are mostly likely to develop through changes due to external loads, which
could be observed at the portals and recesses in the linings (see Figure 2.10). Cracks
seem to be perpendicular to the tunnel axis if there are any changes in the loads or in
the cross-section. Alternatively, longitudinal cracks parallel to the tunnel axis may
appear along the crown or the spring line. The immediate cause of these cracks is
unexpected excessive loads.
Cracks may also develop along the bottom of the tunnel walls, indicating the
settlement of the foundations. Short cracks indicate local overstress, defects in the
lining materials or poor workmanship.
One of the inspections is to monitor the size changes of cracks over a given time.
Traditionally, the cracks’ ends and widths are marked. As such, any changes in
length and width could be measured between markers. (Széchy, 1967)
19
5) Causes of disorders in tunnels
For unlined tunnels, disorders result from loose pieces of rock due to blast or
vibration from locomotives. If rock falls, it may damage or obstruct the track or
cause injury to personnel.
For tunnels with lining support, the main disorders are lining distortions, cracks and
spalling on the tunnel lining.
There are some major causes of disorders in tunnels:
Deterioration due to defective materials and construction methods
Old building materials like soft sandstone and limestone with marl have a much
lower resistance to water, frost, smoke and atmospheric pollution than modern high
strength and well compacted concrete.
Poor construction methods and workmanship can also result in later deterioration.
Particularly in the past, the tunnel lining was not built up immediately against the
excavated ground face and voids between them were poorly grouted or left
ungrouted.
Deterioration caused by water
The influence of water damage in tunnels is enormous which could damage tunnels
in different ways.
Even clean and unpolluted water could dissolve some chemicals, leading to trouble.
For instance, the carbonate and chloride content (CO32-
, Cl-) could invade the
20
concrete and metal structural supports and the sulphate content (SO42-
) may attack
the concrete, the cement mortar or the lime in some lining joints.
One physical hazard from water is a softening action on the surrounding cohesive
materials, which causes a reduction in strength and an increase in compressibility.
For example, excessive settlement could occur as a result of the softening of the
ground under the walls, accompanied by tunnel distortion and cracks in the arch.
In railway tunnels, the most severe damage results from another physical effect of
water. The water resulting from frost would affect not only the quality of the lining
but also that of the railway tracks, partly through the formation of icicles (as water
dripping on the rails and freezing up) and partly through the freezing of the ballast,
which is less elastic and creates unpredictable, uneven support conditions. These
may cause broken rails and derailed trains. Short tunnels suffer more from frost,
particularly near the portals.
Damage due to smoke
Smoke is significantly dangerous to iron members. A large amount of sulphur
dioxide (SO2) is the product of combustion from steam or diesel locomotives and it
greatly accelerates the corrosion of iron in a damp atmosphere. Furthermore, SO2 in
smoke, accompanied by water, gives rise to acid attack on cement and lime.
Damage caused by overburden
The most dangerous overburden form is the actual overburden pressure in deep
tunnels. Deformations and cracks due to actual overburden pressures are likely to
occur in limestone and clay marl tunnels.
21
Tunnel portals are subjected to significant additional pressure because of progressive
weathering and the sliding of the nearby supported slopes (Széchy, 1967).
6) Collapses
Collapse, a major tunnelling instability, is often reported by prior deformation,
cracks, tunnel lining spalling and ground subsidence. Another cause of collapse is
the crossing of undetected weak zones, e.g. faults, discontinuity of rock slopes or old
shafts filled with loose, cohesionless materials and water. Many collapses can be
avoided by installing additional supports such as rockbolts (Kolymbas, 2005).
Table 2.1 clearly shows some of the incidents of tunnel collapse to have occurred
over the centuries in Britain.
22
Table 2.1 Incidents of tunnel collapse through the centuries (Courtesy of
Network Rail Ltd.)
2.2.4 Regular inspection
The crucial work before maintenance is regular inspection for two reasons
(Kolymbas, 2005):
Example of Tunnel Collapses:
Abernant - in 1870’s Poor construction, not solid backed, ground movement
Black-Boy - 1865 Collapse – train ran into it – voids above – dynamic impact
Betchworth - 1887 Unfavourable ground – fine running sand - inadequate lining
St Katherine’s - 1895 Water formed cavity above crown, rotted timbers, brick ring fell
Dove Holes - 1872 Heavy rain, landslip, train hit collapsed tunnel section, several
injured
Bramhope - 1854 Train hit fallen rock/masonry from roof, uncoupled & caused crash
Cockett - 1899 Dewatering mine below, crushing crown bricks, 600Tonne collapse
Bradway - 1922 Filled shafts collapsed into tunnel – rainstorm – single skin brick
lining
LUL - 1922 Tunnel enlargement, wet area of ground, temp works disturbed by
train
Cofton - 1928 Poor construction, uneven loading, works taking place, 4 dead 3
injured
Clifton Hall - 1953 Shaft Collapse – 2 fatalities – houses above collapsed
Duckmanton - 1959 Crown Collapse – voids above - dynamic impact
Penmanshiel - 1979 Geology / Overloaded Lining – during works – 2 killed
Strood - 2002 Chalk Fall – Unlined section – train de-railment
Gerrard’s Cross -
2005
Collapse during construction
23
1) Examination of design work
Certain measurements after construction should be executed to compare the results
with the designed one. If there is a large discrepancy between predicted and
measured values, revised constructions should be added, according to the tunnel
conditions.
2) Indication of incoming hazards
Conventionally, certain inspectors and engineers carry out a series of major
inspection schemes on a yearly basis manually. Regular inspection has been proved
to be an efficient means of identifying potential hazards, e.g. damage and collapses.
The lining part needs to be examined primarily.
2.2.5 Maintenance
A great number of British railway tunnels were built nearly 100 years ago; some are
even older. Over this long period, tunnels have suffered from the frequent vibration
of passing trains and a continuous smoky atmosphere, causing deterioration of the
structures, e.g. the inner surface of the lining.
In the UK, few new railway tunnels are currently under construction. Therefore, the
major work on tunnels is largely concerned with maintenance. For those brick-lined
tunnels with inherently weak bricks, some maintaining methods are listed:
24
1) Spalling of the surface
The usual solution is to cut out the total defective area and substitute with new bricks.
More advanced and efficient ways are proposed such as guniting, using a mixture of
cement, sand and water to spray on the spalling surface under pneumatic pressure.
2) Open joints and the loosening of bricks
Repointing could make up for the defects. Grouting could provide another solution
under appropriate conditions.
3) Cracking and bulging
Minor cracks can be pasted with plaster. Larger cracks need to be monitored over a
period. If there are no further signs of an increase, these cracks could be closed to
avoid more damage (Széchy, 1967).
2.2.6 Summary
Permanent linings are primarily proposed as the structural supports in most tunnels.
Next, instability phenomena in tunnels, particularly lining disorders due to the
ageing phenomenon, are introduced in this section. Some maintenance methods
follow.
25
2.3 Tunnel monitoring methods
2.3.1 General introduction
There are some conventional and progressive non-destructive measuring methods to
monitor tunnel distortions and convergence, as well as the existing state of lining.
The details of these approaches are introduced in the following sections.
2.3.2 Monitoring tunnel distortions and convergence
By setting a series of target points and monitoring them at regular times, the internal
profile of the tunnel could be observed. The deformation status of the profile could
be obtained by comparing the previous profile with the current one.
1) Conventional contact measuring methods
The monitoring of convergence is usually carried out with the help of pins (target
points) fixed on the tunnel wall soon after the excavation. Conventionally, the
distance between pins is measured with invar wire and steel tapes (see Table 2.2).
Tape extensometers (see Table 2.2) are also used to measure the distance between
the target points on the tunnel wall.
2) Non-contact measuring methods
Nowadays, non-contact measuring methods are widely used in measuring work, such
as total stations, an optical tachymeter (or tacheometer) and the photogrammetric
method (i.e. evaluation of stereo images).
For most instruments, the fixed target points describing a cross section could be
recorded, processed and presented as X, Y, Z coordinates. By comparing consecutive
26
images, the information on tunnel displacements and convergence would be obtained
as well as the thickness of the lining support after excavation (Kolymbas, 2005). The
methods are listed below:
Geodetic tachymeter (Total station)
A geodetic tachymeter is an electronic/optical theodolite with integrated device for
distance measuring. It is also called ‘total station’.
Figure 2.11 Monitoring of convergence with a laser tachymeter (Kolymbas,
2005)
The electronic tachymeter works as a combination of an electronic theodolite to
measure angles and an Electro-magnetic Distance Measurement (EDM) system to
read distances from the instrument to a particular point. Optical and laser
tachymeters (see Figure 2.11) share similar principles to perform distance and profile
measurement. The accuracy of the laser tachymeter is more acceptable for many
geodetic applications (Clarke et al., 1992).
Routine geodetic surveying uses total stations to measure the movement of tunnel
walls in three dimensions, with several 3D optical reflector targets (typically at the
27
crown, spring-line and occasionally at the side of the bench) installed at sections
along the tunnel (e.g., 15 – 20 m between sections). The measurement of these
targets is gained by placing the total station on the brackets bolted on the tunnel wall
and moving the instrument forward. The coordinates of the targets are obtained from
each instrument position. Any deformation of the tunnel would be noticed at regular
tunnel inspections. Due to fuel emissions or dust, the precision of the measurements
might be reduced in tunnels (Kavvadas, 2005).
Tunnel profilometer
Figure 2.12 Typical features of the DIBIT tunnel profilometer (Kavvadas, 2005)
As digitised photogrammetric measuring instruments, tunnel profilometers (or tunnel
scanners) are applied to measure the profile of tunnels with the help of powerful
uniform illumination. There are two CCD (Closed-circuit Digital) cameras fixed on a
portable frame in the system (see Figure 2.12). Digital images are taken and
automatically stored in a field computer. Then, 3D coordinates of the surveyed
tunnel surface are provided after processing with an accuracy of ± 5 mm. Although
this level of accuracy is low compared to routine geodetic surveying (± (2 - 3) mm,
28
see Table 2.2), the advantage of recording a very large number of points on the
tunnel wall can outweigh the low accuracy for many applications (Kavvadas, 2005).
Profile-image method
Figure 2.13 Illustration of imaging geometry of profile-image method for the
tunnel wall (Wang et al., 2010)
Wang et al. (2009) have proposed a profile-image method to improve the precision
and speed of the tunnel profile measurement. A line laser device is used as
illumination to beam any profile along the tunnel. Using a digital camera, six
calibration points with known coordinates in space down the tunnel can help to
determine the relative six points with coordinates located on the same plane of the
laser-lit profile, in one image. Thus, a profile of any section of a tunnel can be
obtained (see Figure 2.13).
29
This method could measure the profile more precisely under poor conditions, such as
a moist environment. The limitations should be addressed in future work, for
example, the diffusion of a laser beam (width of the beam) when applied in a large
tunnel (Wang et al., 2010).
Similarly, the LaserFleX™ system (see Figure 2.14) mounted on a vehicle offers a
continuous structure profile measurement (Balfour Beatty Rail Ltd., 2006).
Figure 2.14 Examination in process using LaserFleX™ (Courtesy of Balfour
Beatty Rail Ltd.)
Summary
The resolution and system accuracy of these profile-measuring methods are listed in
Table 2.2 (Kolymbas, 2005; ES&S Ltd., 2009; Leica Geosystems Ltd., 2009).
30
Table 2.2 Methods for monitoring of convergence
2.3.3 Identifying damaged defects on tunnel shells
One of the main tasks in tunnel examination is to identify all types of defects in the
whole tunnel shell, such as leaks, cracks, corrosion, cavities and water seepage. Here
are some common methods:
1) Conventional contact measuring methods
The tunnel profile is usually divided into 5 parts: the crown, two upper sidewalls and
two lower sidewalls. One inspector is responsible for detecting one part of the tunnel.
The tunnel lining is tapped with a hammer to identify loose bricks, internal voids,
hollowness, cracks, damp patches, bulges or any other defects as Figure 2.15 shows
(Péquignot, 1963).
Method Manufacturer Resolution (mm) System accuracy
(mm)
Invar wire SolExperts 0.001 ± 0.003
Steel tapes Interfels 0.01 ± 0.05
Tape extensometer ES & S 0.02 ± 0.02
Geodetic
tachymeter e.g. Leica 1 ± (2 - 3)
Tunnel
profilometer
DIBIT,
GEODATA 1 ± 5
Profile-image
method ± (5 - 10)
31
Figure 2.15 Manual work with devices (Courtesy of Network Rail Ltd.)
2) Non-contact measuring methods
There are several types of non-contact and non-destructive investigation techniques
for identifying defects. These include:
a) Mechanical oscillation techniques
b) Radiation techniques
c) Electric and electronic techniques
d) Optical techniques
Each type consists of several techniques, listed in Table 2.3.
32
Table 2.3 Advantages and disadvantages of various techniques for existing non-
destructive investigation of tunnels (Haack et al., 1995)
Techniques Mainly
Applied for:
Value for
Tunnel
Application
Problems
With: Advantages
Mechanical
Oscillation
Techniques
Structural
dynamic
methods
(direct
vibration)
Bridges;
buildings
aboveground
Very low
Uneven wall
thickness;
rock in
homogeneity;
varying
groundwater
level
None
Seismic
reflection
Geological
investigation;
determination
of layer
thickness
Low Accuracy;
speed
Only
connected
with very
large cavities
behind the
tunnel lining
Micro
seismics and
sonic
emission
analysis
Coal mines;
laboratory tests Very low
Reproducibili
ty; accuracy
Investigation
of structure-
borne noise
Ultrasonics
–reflection
and indirect
surface
transmission
Steel
construction;
mechanical
engineering;
pipelines; tanks
Very low
Coupling to
test ground,
concrete
inhomogeneit
y; speed of
diffusion by
aggregates;
accuracy
None
Radiation
Techniques
Gamma ray
backscatter
Road
construction,
earth
construction;
investigation of
moisture
content and
density
Very low
Speed;
penetration
depth
None
Neutron
backscatter Low
Speed,
penetration
depth
Indication of
moisture
content point-
by-point
33
Techniques Mainly
Applied for:
Value for
Tunnel
Application
Problems
With: Advantages
Electric
and
Electronic
Techniques
Eddy current
methods
Electricity
conducting
metals; crack
detecting for
pipelines,
indication of
reinforcement
Low
Speed, non-
conducting
materials;
penetration
depth.
Indication of
reinforcement
Georadar
Ground
investigation of
bridges and
tunnels
High
Evaluation;
reflection by
metallic
cladding;
speed
Good
penetration
depth
Electrical
potential
methods
Detection of
corrosion of
reinforcement
Low
Speed;
penetration
depth
Detection of
corrosion
Optical
Techniques
Infrared
thermography
combined
with visual
determination
Check of
thermal
insulation;
tunnels
Very high
Certain
tunnel
climates;
evaluation;
heat release
of
installations
Detection of
cavities and
moist patches,
cracks, etc.;
high speed
Multispectral
analysis
Monuments,
buildings,
tunnels
High
Speed;
vibration;
demand of
powerful
lighting;
evaluation;
penetration
depth
Detection of
small and dry
cracks
34
3) Highly valuable techniques for tunnel investigation:
The highly valuable methods (Georadar, Infrared thermography and Multispectral
analysis) for tunnel application, as shown in Table 2.3, are discussed in the following
sections:
Georadar
In principle, georadar can detect anomalies in ground mass or structures like bridges
and tunnels and can identify defects by noticing variations in the transit times for the
reflected signal.
Since the reflection angle of the georadar unit is around 60°, defects could be
identified before the georadar is located above. As the georadar moves towards one
defect, the signal’s transit times become shorter and shorter. The transit times would
increase again as the georadar moves away from the defect. Finally, a transit time
curve is obtained, showing a defect. However, not all of the disturbances showed
were really damaged. In some other cases, defects could not be identified. (Haack et
al., 1995).
Infrared thermography
Some tunnels have been investigated using an infrared scanner. The scanner makes
full use of infrared thermography technology. It is an optic-electronic measuring
device installed on a moving vehicle (see Figure 2.16). The scanner basically surveys
the whole part of the tunnel lining. Moist patches in the tunnel shell and water
seepage behind the tunnel shell could be recognised (Haack et al., 1995).
35
The use of georadar and infrared thermography for the inspection of a tunnel remains
uncertain and incomplete with regard to the detection of defects. Some defects, such
as corrosion and dry cracks cannot be detected properly (Haack et al., 1995). Thus,
there is a need to develop investigatory methods.
Figure 2.16 Tunnel inspection using an infrared scanner (Haack et al., 1995)
Multispectral analysis
In the process of multispectral analysis, photos of a surface are taken in a similar
way to colour photography. Normally, there are six filters to separate some spectral
areas from the entire light spectrum. For the same section of a structure, one shot is
taken per filter.
36
A multispectral projector is used to superimpose these pictures taken of the same
section with different filters. In this way, information about the surface areas would
display a change in colour, thereby revealing some surface defects that are invisible
to the human eye. Multispectral analysis has been employed to detect lining cracks in
experimental tests by highlighting the thin cracks as bright lines against a dark
background. The high resolution of this method could detect fine cracks as small as
0.5 mm. In addition, more defects, such as moist patches and deposits of carbonate
could be recognised.
The multispectral analysis method may be excellent for identifying fine cracks in
tunnel shells but it could not widely cover most work of defect inspection in tunnels
(Haack et al., 1995).
Discussion
A series of tests on an experimental wall (Haack et al., 1995) used the above three
methods respectively. It indicated that these three methods do complement one
another for tunnel defect inspection. Under certain circumstances, it was advisable to
use all three methods, which seemed to be relatively complex. Due to the limitations
of these methods, more efficient and advanced techniques for tunnel examination are
needed with some requirements:
a) High speed
b) High accuracy
c) Detection of all kinds of defects
In the following section, two advanced techniques (A laser scanning system and
photogrammetry) are proposed for inspecting defects on tunnel shells.
37
4) Laser scanning system (LiDAR)
Figure 2.17 The principle of Lidar
Technology description
The use of laser scanners to determine distances to objects is based on a similar
principles as ordinary radar, although ‘laser radar’ or ‘Lidar (Light Detection and
Ranging)’ systems send out a narrow pulsed beam of light rather than broad radio
waves (Figure 2.17). The systems uses the principle of either phase measurement or
the speed of light and very precise timing devices to calculate the distance between a
laser emitter/receiver device and an object reflecting the beam (Turner et.al, 2006).
Horizontal direction and vertical angle to the target point are recorded as well.
A series of closely spaced target points on the object are targetted by the laser
scanner and located by the range and orientation from the instrument position. The
devices are capable of generating dense “clouds of points” that could be processed to
yield three-dimensional [x, y, z] coordinates of the features being scanned. These
ground-based laser scanners do have a benefit as being able to measure vertical, or
(x,y,z)
Origin of
measurement
system (0,0,0)
Vertical angle
Horizontal dimension
Range
38
near-vertical objects that could not be visible so cannot be accurately measured from
airborne sensors (Turner et.al, 2006).
A major advantage of this technique is that real objects can be represented more
adequately in three dimensions than the use of a single picture or collection of
pictures. Scanning can also provide a higher level of detail together with good metric
accuracy. It operates automatically and without any contact (Guarnieri et.al, 2004).
Current applications
Figure 2.18 A typical laser scanner (Courtesy of Plasser American Ltd.)
Laser scanning technology seems to be a very promising alternative for many kinds
of surveying applications. Airborne and ground-based laser scanners acquire a huge
amount of 3D data very quickly, which can be profitably combined with coloured
high-resolution digital images to provide a 3D representation of the environment.
These models are currently used for cultural heritage, industrial, land management
and also medical applications (Guarnieri et.al, 2004).
For distance measurement, a semi-conductor laser in the sensor head is modulated
with high frequency in a sine-wave form and guided vertically upward by means of
an oscillating mirror. When the laser beam hits the contact wires to be measured
and/or other objects, it is reflected and the phase shift is measured by a detector.
39
Then the distance can be calculated from the phase shift of the emitted and reflected
laser light (Plasser American Ltd., 2010).
To measure the horizontal position the laser beam is deflected laterally by ± 35° by
means of a mirror oscillating at 50 Hz. The specific distance is then measured in
relation to the associated angle. The horizontal position can be calculated from the
determined distance and angle (Plasser American Ltd., 2010). This is also similar to
the measurement of the vertical position.
Current railway applications
A high-speed and non-contact measuring system by laser scanners has been set up.
Typically, the laser scanner is used for (Plasser American Ltd., 2010):
a) Track geometry measurement (track gauge, longitudinal level of both rails, cross
level, twist)
b) Measuring speed
c) Rail profile measurement (corrugations, rail breaks or rail joints, worn-down
welds, ball indentations, wheel burns, missing clips or fastenings), of which
railway structures include tunnels, overbridges, under-bridges, platforms, signals
and station canopies.
d) Ballast profile measurement
e) Clearance gauge measurement
f) Geometrical measurement of the contact wire (height and stagger of contact wire,
the position of catenary masts, the position of distance marking and the position
of structures such as bridges)
40
Potential applications
There is potential for monitoring the performace of objects such as tunnel
deformation, automatic calculation of embankment/cutting slopes and angles,
vegetation coverage, tree positioning, all which would be of benefit to the railways.
Further research and development
Future work could focus on the development and comparison of processing
algorithms in order to improve the accuracy of the surface displacement maps
(Schulz et al, 2005).
Further evaluation of 3D laser scanner development and data analysis procedures are
needed, conducting instrument comparisons with field-testing facilities, which have
been used to test some well-documented rock slopes and to verify laser data
collection procedures.
Additional experiments should be undertaken to compare ground and airborne laser
scanning data to determine the scale effects. It is also important to study the
advantages of integrating laser scan data with the interpretation of optical imagery
further, especially the high-resolution digital photographs now available with several
scanners.
Of further interest is to investigate whether the intensity of the reflected laser returns
in combination with information on the orientation can for example on a local rock
surface, provide information that might assess the roughness and weathering of
individual discontinuity sets (Turner et.al, 2006).
41
5) Photogrammetry
Technology description
Photogrammetry is the technique of measuring objects (2D or 3D) using photographs,
which may also be imagery stored electronically on tape or disk taken by video,
digital cameras or radiation sensors, such as scanners. The most important feature is
the fact that the objects are measured quickly without being touched. Therefore, the
term ‘remote sensing’ is sometimes used instead of photogrammetry. (see Figure
2.19) It is a well establish technology although digital photogrammetry has made
significant benefits in automation of the techniques (Mcglone et al., 2004)
Figure 2.19 The principle of photogrammetry (Courtesy of Geodetic Systems
Ltd.)
Classification of photogrammetry
Principally, photogrammetry can be divided into two groups.
a) Depending on the lens-setting:
o Far range photogrammetry (with camera principal distance/focal length
setting to infinity)
42
o Close range photogrammetry (with camera principal distance/focal length
settings to finite values).
b) Another grouping could be:
o Aerial photogrammetry (mostly far range photogrammetry)
o Terrestrial photogrammetry (mostly close range photogrammetry).
Figure 2.20 Digital cameras at different positions in photogrammetry (Courtesy
of Geodetic Systems Ltd.)
Photogrammetry uses several camera stations located in different places and
associated with custom-calibrated lenses and cameras to optimise the intersective
geometry of the light rays (see Figure 2.20). Mathematical techniques are used to
complete the coordinates of the points at the interesting rays and optimised positions
are calculated when redundancy of measurements occur.
43
Current applications
The applications of the photogrammetry technique are widespread nowadays. The
technique is mainly utilised for object interpretation and measurement.
In civil engineering, it has provided useful information on the cracking behaviour of
reinforced concrete, including crack width, displacement, etc. under different loading
conditions (Pease, 2006) as well as short and long time load tests of civil engineering
materials (Hampel, 2003).
Photogrammetry is used as a fundamental tool to generate Digital Terrain Models
(DTMs) without any objects like vegetation and buildings, starting from Digital
Surface Models (DSMs) (Bitelli et al., 2004). From the images taken, it is possible to
generate DTMs and DSMs of objects (e.g. topographic surfaces, road mapping,
historical heritage modelling), contours, cross-sections, as well as joint and minor
fracture zone orientations, etc. (Martin et al., 2007).
Aerial photogrammetry is mainly used to produce topographical or thematical maps,
engineering surveys, digital terrain models and to provide a good source of historical
data. The users of close-range photogrammetry are often architects and civil
engineers (to supervise buildings, document their current state, deformations or
damages), archaeologists, surgeons (plastic surgery) or police departments
(documentation of traffic accidents and crime scenes), to mention just a few.
Current railway applications
Photogrammetry has mainly been applied to measure rail tunnel profiles as well as
deformation mornitoring. The applications have been viewed with great interest as
44
the DTMs have a variety of further uses: landslide prediction, slope measurement
and heights of embankments, rolling stock clearence, etc. It is also possible to
generate models oftracks, rails and infrastructure.
Further research and development
An improvement of photogrammetry is considered in further study with lasers to
measure the profile and deformation of tunnels, especially in bad conditions
(penetration, dirt, degragation and erosion, etc.)
2.3.4 Final discussion
Conventional contact inspection procedures still play an essential role in the
monitoring of tunnels. They might be accurate enough, but they are rather time-
consuming, potentially destructive to tunnels and easily affected by human errors etc.
The advanced and automated non-contact testing methods, such as digital
photogrammetry and laser scanners could improve or substitute conventional tunnel
inspection procedures.
2.4 Masonry structure review
2.4.1 Introduction to masonry structures
As one of the most popular and oldest architectural materials, masonry plays an
important role, particularly in tunnels, bridges and historical buildings.
This research focuses on the numerical modelling of old brick-lined tunnels. As a
masonry structure, the brickwork forms the tunnel support. Trying to understand and
simulate the brickwork ageing process is challenging. Therefore, it is worthwhile
45
starting by understanding more about the properties of brick, mortar and the
composite brickwork separately in the following section.
2.4.2 Brick bond patterns
1) Brickwork wall
Terms of brickwork wall
Before introducing various types of bond patterns, terms with general application to
brickwork should be reviewed, as defined by McKay (1968).
Bed: The lower surface of a brick when placed in position;
Header: The end surface of a brick;
Stretcher: The side surface of a brick;
Face: A surface of a brick, such as the bed face, header face and stretcher face;
Course: A complete layer of bricks; a heading course consists of headers and a
stretching course comprises stretchers;
Bed joints: Mortar joints, parallel to the beds of the bricks and therefore horizontal in
general walling;
Cross or vertical joints: These are between the ends of bricks in general walling,
perpendicular to the beds of the bricks.
46
Different types of brickwork wall
Five popular bond patterns of brickwork wall are listed below (1, McKay 1968) and
illustrated in Figure 2.21.
The American, or common bond: It is a variation of the stretcher bond. This bond
has a course of full-length headers at regular intervals that provide the structural
bond as well as the pattern. Header courses usually appear at every fifth, sixth or
seventh course, depending on the structural bonding requirements.
English, or cross bond: It consists of alternating courses of headers and stretchers.
It is the strongest bond as the bricks are well lapped. Each alternate header is
positioned centrally over a vertical joint.
Flemish bond: This comprises alternating headers and stretchers in each course. The
headers in every other course are positioned centrally over and under the stretchers
in the courses in between. It is not as strong as English bond due to the large number
of short, continuous joints.
Stack bond: There are no overlapping units in any course and all vertical joints
alignment. This pattern usually bonds to the backing with rigid steel ties, when
available.
Stretcher or running bond: This consists of stretchers in every course. Since the
bond has no headers, metal ties are usually employed to form the structural bond.
47
Figure 2.21 Different arrangements for brick masonry: (a) American bond; (b)
English bond; (c) Flemish bond; (d) Stack bond; (e) Stretcher bond. (Lourenço,
2008)
2) Brick arch
General introduction to the brick arch
A typical brick arch consists of wedge-shaped bricks jointed with mortar and spans
an opening. It supports the weight above to a large extent by transmitting the
pressure downwards to the bottom, thus constituting a comprehensive application in
the architecture and engineering fields.
Terms of arches
Common terms of arches are shown below (McKay, 1968).
Ring or Ring Course: The circular course or courses comprising the arch;
Extrados: The external curve of the arch;
(a) (b)
(d) (e)
(c)
48
Intrados: The inner curve of the arch;
Face: The outer surface of the arch between the intrados and extrados;
Crown: The highest point of the extrados;
Bed joints: The joints between the bricks, which radiate from the centre;
Voussoirs: The wedge-shaped bricks that comprise an arch;
Key brick: It is the central voussoir in a brick arch, which is usually the last voussoir
to be placed in position. The key shown in the middle picture of Figure 2.22
comprises two bricks.
Classification of brick arches
McKay (1968) classified brick arches according to their shape and the materials and
workmanship employed in their construction.
a) Shapes — including flat, segmental, semi-circular, circular, semi-elliptical,
elliptical and pointed types.
b) Materials and Workmanship — consisting of either rubber bricks (coloured soft
bricks, made of rubber), purpose-made bricks, ordinary or standard bricks cut to
wedge shape (axed bricks), or standard uncut bricks (rough bricks).
This research concentrates on a rough brick semi-circular arch to form a horse-shoe
tunnel (see Section 3.5 in details).
49
Different types of semi-circular brick arches
Figure 2.22 Different kinds of semi-circular brick arches: (a) Multiple-ring
arches with uncut rectangular bricks; (b) Multiple-ring arches with wedge-
shaped bricks laid in radial orientation; (c) single ring arch
Figure 2.22 shows three common semi-circular arches of railway tunnels. This
research uses a similar arch type to the one as shown in Figure 2.22 (a).
2.4.3 Brick/Mortar/Brickwork properties
1) Brick properties
Physical properties
The dimensions and dry mass density of each brick type are slightly different. The
dimension of a normal brick would not exceed 337.5 × 225 × 112.5 mm (L × W × H).
The discrepancy between the dimensions of bricks from one batch would normally
not exceed 0.5% of the average dimension. Bricks may be wire cut, with or without
(a) (b) (c)
50
perforations, pressed with single or double frogs or cellular (Vermeltfoort et al.,
2005).
During the manufacture of bricks, countless fine pores are formed inside which
influence almost every important property of the brick, such as compressive strength,
modulus of elasticity, thermal conductivity, moisture expansion and frost resistance.
The term porosity is used to represent the volume of pores out of the overall volume
of the brick substance (Lenczner, 1972).
The water absorption properties of bricks are rather important for mortar workability
and bonding. As such, the Initial Rate of Absorption (IRA) and total absorption are
established for each type of brick. The IRA is measured for a unit in the first minute
that it is immersed in water. Some research has shown that the IRA was inconsistent
in relation to the bond. Therefore, it is usually recommended that the total absorption
is used since this seems to be more appropriate (Sutcliffe, 2003).
In this way, the long-term suction properties could also be established by registering
the water quantity absorbed over a given period. These absorption quantities may be
able to give an indication of the pore volume of the brick (Vermeltfoort et al., 2005).
Elastic properties
The stress/strain relationship of a brick is almost linear up to the point of fracture.
Young’s modulus of bricks varies from 3.5 kN/mm2 to 34 kN/mm
2. (Lenczner, 1972)
Compressive properties
Different manufacturing approaches and procedures produce different brick
structures with different strengths. For instance, the final strength of material such as
51
clay-brick depends on the final temperature. The higher the temperature is, the
higher the strength will be, since more minerals melt.
The compressive strength of bricks could be tested with a brick unit or several layers
of bricks glued together, which are then loaded on the bedding surface and the brick
face. The deviation in strength is believed to be due to the anisotropy in the material
(Vermeltfoort et al., 2005).
Tensile properties
Due to the relatively high porosity and brittleness of bricks, the tensile strength is
generally weak (Lenczner, 1972).
Detailed tensile tests could be tested on single bricks, providing lateral confinement
at the end of the specimen (Vermeltfoort et al., 2005).
Durability of bricks
The durability of bricks is closely related to the resistance to chemical attack,
moisture penetration and frost action. Among the agents causing chemical attack,
efflorescence is probably the most common one. Salt is an essential material for
efflorescence. Soluble salts contained in most clay bricks, combined with water
could increase the occurrence of efflorescence. The sulphate, carbonate or chloride
content (SO42-
, CO32-
, Cl-) of other agents like soot or water could also attack the
bricks (Lenczner, 1972).
52
2) Mortar properties
Physical properties
Modern masonry mortars are often made of cement, lime (conforming to BS 890),
sand and water in specific proportions (Sutcliffe, 2003).
Elastic properties
The elastic properties of mortar would significantly affect the elastic properties and
strength of the brickwork. The compressive strength of a brick is greater than that of
mortar. When bricks and mortar are bonded together as brickwork, they are forced to
strain equally, causing the bricks to move into a state of tension (Lenczner, 1972).
Compressive properties
Mortar compressive strength is affected by the cement content of the mix, the
water/cement ratio, the proportion of cement to sand and the properties of the sand.
For instance, high cement content and a low water/cement ratio would yield a
mixture of high compressive strength. To some degree, coarse sand seems to yield at
a higher strength than fine sand (Lenczner, 1972).
The curing (moisture) conditions of the mortar affect its mechanical properties.
Mortar that is too dry or too wet has a negative effect on strength (Vermeltfoort et al.,
2005).
Tensile properties
The tensile bond strength is the adhesive strength between the mortar and the brick,
and is influenced by both of them. The tensile strength is typically measured by
53
separating sandwich brick assemblies in the laboratory to determine the tensile force
(Lenczner, 1972).
Durability of mortars
The presence of excess calcium chloride in mortar may accelerate its deterioration
and encourage efflorescence. The mortar may also suffer from sulphur compounds in
a smoky atmosphere. It is advisable to mix sulphate resisting Portland cement in
mortar for better durability.
3) Composite brickwork properties
The properties of the composite strongly depend on the properties of the components:
the brick, the mortar, and their complex interactions (Sutcliffe, 2003). Unreinforced
brickwork was tested under different loading conditions to study the behaviour.
The strength of brickwork in compression
The failure mechanism of brickwork under vertical stress is illustrated in Figure
2.23. When under a great axial compression load, lateral strains are experienced by
both brick and mortar. Since strains in mortar are normally larger than those in
bricks, the brick is consequently put into a state of lateral tension and the mortar into
lateral compression.
Typical failure in brickwork may occur in the form of vertical splitting as the tensile
stress in the brick reaches its ultimate tensile strength (see Figure 2.24).
54
Figure 2.23 Lateral expansion of brick and mortar under vertical stress
(Lenczner, 1972)
Figure 2.24 Typical failure pattern in a brickwork wall (Lenczner, 1972)
Here are the main factors affecting the compressive strength of brickwork:
The strength of the bricks: Hendry et al. (1998) observed that the compressive
strength of brickwork was smaller than that of the bricks given by a standard
compressive test. Furthermore, Lenczner (1972) indicated that the brickwork
Compressive strain
in mortar
Tensile strain
in brick
Free lateral expansion
of brick
Free lateral expansion
of mortar
55
strength was almost proportional to the square root of brick strength after tests at 28
days.
The strength of the mortar: The brickwork strength is much higher than the cube
crushing strength of the mortar used (Hendry et al., 1998). The strength of brickwork
is approximately proportional to the fourth root of mortar strength with constant
brick strength (Lenczner, 1972).
Other factors: A number of other factors would affect brickwork compressive
strength; for example, the density of bricks, the dynamic modulus of the mortar, time
of curing, thickness of mortar bed joints, water suction of the bricks, the brickwork
bonding pattern and workmanship (Lenczner, 1972).
The strength of brickwork in tension
Tensile failure modes of brickwork in uni-axial tension parallel or perpendicular to
the bed joints are listed below (Sutcliffe, 2003):
a) Crogged or stepped tensile failure of joints (Mortars weaker than bricks - see
Figure 2.25 (a))
b) Vertical tensile failure of bricks and joints (Bricks weaker than mortar - see
Figure 2.25 (b) and (c))
c) Horizontal bed joint tensile failure of mortar joints (Weak mortar and brick /
mortar bond - see Figure 2.25 (d))
56
Figure 2.25 Tensile failure modes (Sutcliffe, 2003)
The tensile bond strength of brickwork is dependent on (Sutcliffe, 2003):
a) Suction of the bricks and water retention of the mortar
b) Mortar composites
c) Workmanship, including fullness of joints and cleanliness of jointing surfaces
The strength of brickwork in shear
Shear strength is critical for brickwork walls under lateral loads. The possible failure
of a masonry shear wall would occur in such modes (Lenczner, 1972; Sutcliffe,
2003):
a) Direct tensile failure at the wall heel
b) Shear sliding along a bed joint
c) Diagonal tensile failure of the wall
a. Crogged failure of joints
d. Vertical tensile failure of bricks and joints
c. Vertical tensile failure of bricks b. Horizontal bed joint failure of joints
57
d) Compressive or crushing failure at the wall toe
Mohr-Coulomb relationship in Equation (2.1) could deduce that:
The resistance of brickwork to horizontal shear would increase as the normal load
increases.
The shear strength of the joint is also highly related to both shear bond strength (c)
and friction between bricks and hardened mortar.
……………………………………...………………………..… (2.1)
Where
Joint shear strength;
Shear bond strength;
Coefficient of friction;
Compressive stress normal to the joint
Many factors affecting the tensile bond strength of brickwork are also related to the
shear bond strength (c) of brickwork (Sutcliffe, 2003):
Brick properties: Compressive strength, roughness of the contact surface, suction
(initial rate of absorption and total absorption) and moisture content;
Mortar properties: Compressive strength, mortar composites and ratios, flowability,
water retentivity;
58
Other factors: Brickwork prism compressive strength, joint thickness, curing
conditions.
2.5 Numerical modelling review
2.5.1 Introduction to numerical simulation strategies
There are three basic numerical simulation approaches for masonry structures at
present (Idris et al., 2008), as can be seen in Figure 2.26.
1) Detailed micro-modelling
Bricks and mortar in the joints are represented by continuum elements, while the
brick / mortar interface is represented by discontinuous elements.
2) Simplified micro-modelling
The continuum part of detailed micro-modelling expands to zero thickness interfaces.
3) Macro-modelling
The brickworks are assumed to be on an equivalent continuum.
Both simplified micro-modelling and macro-modelling are to be used in this research
and compared with each other.
59
Figure 2.26 Basic approaches to masonry structures (Idris et al., 2008)
2.5.2 Numerical analysis of masonry structures
Numerical analysis of masonry structures in tunnels, bridges and buildings is
presented in the following sections:
1) Numerical analysis of masonry tunnels
Introduction
In tunnelling, numerical models are built to analyse and predict the mechanical
behaviour of the surrounding areas, the support (e.g. linings, rockbolts) and the
ground. Thus, the stability of tunnels could be assessed efficiently for optimum
construction as well as maintenance. Numerical simulations are also used for
sensitivity analyses to show the effects of different parameters on tunnel stability.
However, the results by numerical simulation are not convincing without being
validated. The validation process is often undertaken by experimental work.
Therefore, the preparation of physical model tests in the laboratory is necessary to
simulate the failure of real world tunnels for validation.
(a) Detailed micro-modelling; (b) Simplified micro-modelling; (c) Macro-modelling
Mortar Expanded Unit Homogenised Continuum
Unit / Mortar Interface Zero Thickness Interface
Unit
60
Masonry structures, typically stone blocks and brickworks support the majority of
old tunnels. Due to the vaulted section shape of these tunnels (see Figure 2.27), the
masonry structure is mainly loaded in compression.
Figure 2.27 A typical vaulted masonry tunnel (Idris et al., 2008)
Literature review
Although several modelling approaches to masonry structures are currently under
development by researchers, there are few publications focussed on the analysis of
ancient tunnel masonry structures.
A tunnel masonry structure is a discontinuum, which consists of blocks bonded to
each other by mortar in the joints. Furthermore, there is an interface between the
surrounding soil and the masonry structure. Three basic modelling approaches
(detailed in Section 2.5.1) to masonry structures have now been identified (Idris et al.,
2008).
The well-known Universal Distinct Element Code (UDEC) was proposed by Idris et
al. (2008 and 2009), based on the Distinct Element Method (DEM), to develop old
61
tunnel models supported by masonry structures. The mechanical behaviour of
masonry blocks (limestone) and joints structures were analysed as well. A simplified
micro-modelling strategy was used in the two papers (Idris et al. 2008, 2009).
Idris et al. (2008) used different values of block (limestone) parameters that would
define block failure, such as cohesion, tensile strength and friction angle to simulate
various stages in the tunnel ageing process for degradations. It also allowed the study
of their individual influence on masonry behaviour from elastic to plastic, as well as
the effect of the interaction between these factors (using SURFER 8 software,
multivariate analysis of variance and multiple linear regressions). Whereas soil and
joint properties remained unchanged, block properties such as density, elasticity
modulus (Young’s modulus) and Poisson’s ratio were modified due to underground
water penetration.
The following paper (Idris et al., 2009) focussed on the evolution of masonry joints
to enhance the database of old tunnel instabilities. The study process was similar to
that of the previous paper by changing three joint parameters influencing the
mechanical behaviour of joints. In addition, an experimental design dealing with the
evolution of the normal stiffness/shear stiffness ratio was proposed based on the
UDEC code. Future work could place an emphasis on the study of the influence of
the surrounding soil properties on the ageing phenomenon of tunnels.
62
2) Numerical analysis of masonry bridges
Similar to old masonry tunnels, a large number of arch bridges (see Figure 2.28) in
service were built during the 19th
century. Therefore, they have shown signs of
deterioration.
Figure 2.28 A typical multi-ring arch bridge (from Arthurs Clipart, Org., 2012)
Estimation is necessary to assess their actual load carrying capacity and collapse
mechanism by setting up numerical models. The non-linear finite element technique
(Betti, 2008) and the discrete element method, or a combination of both, showed the
final potential of the arch bridges (e.g. see Figure 2.29). The onset of delamination
could be predicted.
Figure 2.29 Block failure mechanisms of multi-ring arch bridge
63
3) Numerical analysis of masonry building structures
A series of studies have been conducted by many researchers on historical masonry
building structures, which may help to obtain a better understanding of masonry
structures using different numerical modelling methods.
Giordano et al. (2002) proposed and compared several numerical approaches to the
modelling of historical masonry structures. Namely, the standard finite element
method (FEM) modelling strategy was used, assuming homogenized material when
the global behaviour of a whole structure was investigated. When study of the
structure in detail was required, two approaches were proposed: the finite element
method with discontinuous elements (FEMDE) and the discrete element method
(DEM) (see Figure 2.30).
Mechanical behaviour of the control of cracking phenomena after structural
repointing of the bed joints was analysed by Valluzzi et al. (2005) using finite
element models.
64
Figure 2.30 (a) Masonry building: Cloister Façade; (b) DEM internal finite
element mesh of the lower part of the building (Giordano et al., 2002)
2.6 Chapter summary
This chapter is comprised of the basic literature review relevant to the research work,
starting from stability issues of tunnels in which the permanent liners of tunnels and
instability phenomena were reviewed, followed by some maintenance methods. Then,
the typical monitoring methods in tunnels were introduced and compared with each
other in order to find the proper measuring methods for this project. For the purpose
of understanding the materials of brick-lined tunnels in this research, masonry
structures, especially brickwork, were studied in detail. At the end of this chapter,
the numerical modelling strategies were introduced, followed by some reviews of the
numerical analysis of masonry structures.
The details of the physical model preparation, installation and loading tests as well as
post-processing work of monitoring techniques are shown in Chapter 3.
65
CHAPTER 3 PHYSICAL MODEL TESTS
3.1 Introduction
Although numerical modelling continues to be widely used for analysing and
predicting mechanical behaviour of engineering structures, outputs of the majority of
masonry structure simulations have hitherto been unconvincing. It is because of the
ambiguous and inconsistent nature at times of the input data for masonry properties,
and assumptions such as simplified numerical models and interface issues
underlying the models utilised (Jia, 2010). Physical model testing in the laboratory is
an invaluable means of masonry research, not only demonstrating the performance of
real masonry structures, but also validating and confirming the outputs of numerical
models. It is particularly useful to undertake physical model testing prior to
undertaking real world tunnel construction for safety and economic reasons.
A review of existing literature revealed that physical model testing of masonry arch
bridges is not a new concept. Hogg (1997) assessed the effects of repeated loading
on masonry arch bridges (spanning 2.5m) and its implications for serviceability limit
state. Furthermore, Alonso (2001) compared the results from similar tests of half-
scale physical masonry arch bridges (spanning 1.25m) to Hogg’s prototype.
However, there are few publications focussed on the structure analysis of tunnel
masonry structures with verification of physical modelling, alongside the numerical
modelling. In this investigation, the stability of brick-lined tunnels was assessed via
the mechanical testing of physical models constructed in the laboratory under
controlled conditions. In other words, tunnel performance was assessed by applying
incremental loads until the model tunnels failed.
66
3.2 Design of physical model tests
The purpose of conducting different physical model tests on small-scale brick-lined
tunnels was to primarily gain an understanding of the mechanical behaviour of
masonry tunnels in general and in the process determine their respective ultimate
loading capacities. With this knowledge, it became possible to develop a numerical
model capable of predicting the behaviour of real masonry tunnels. It is noted that
the brick-lined tunnels were surrounded by dry sand (soil) to apply surrounding
pressure and allow loading from the top the overburden soil. The soil material is
easier to be obtained and worked with than the rock material in the laboratory.
Several factors were known beforehand to have potential to significantly influence
the outcome of the tests on the physical models. These included brick bond pattern,
the water content of the surrounding soil, brick variability, mortar variability,
surrounding soil type, and load types e.g. concentrated and uniformly distributed
loads. This research focussed on studying the effect of varying the mortar mix
proportions and loading types while the other aforementioned variables were kept
constant for all the different model tests. Details of the variables examined as mortar
mix proportions and loading types are shown below.
3.2.1 Mortar mix proportion
For the first model, a comparatively higher strength mortar mix comprising cement,
lime and sand in respective proportions of ratio 1:1:6 as prescribed by BS 4451:1980
British Standard for Methods of testing mortars, screeds and plasters was used. For
the other physical model tests considered in this study, a mortar mix proportion of
67
lower strength (1:2:9) was used to study the effects of lower strength of brickwork
on the tunnels.
3.2.2 Loading style
In order to simulate the behaviour of both deep seated (e.g. mountain tunnels) and
shallow tunnels subjected to traffic load, the physical model tests were subjected to
static uniform and concentrated load applied to the surface of the overburden soil.
3.2.3 Test variations
As mentioned above, three physical models with varying mortar mixes (1:1:6/1:2:9)
were designed and conducted. The models were monotonically loaded to failure with
uniform and concentrated loads, separately.
Table 3.1 below shows the different combinations of variables investigated for the
three physical model tests conducted.
Table 3.1 Different physical model tests
Mortar mix proportion loading style
Physical model test 1 1:1:6 (higher strength) Uniform load
Physical model test 2 1:2:9 (lower strength) Uniform load
Physical model test 3 1:2:9 (lower strength) Concentrated load
68
3.3 Design of a physical model
3.3.1 General introduction
In this research, the design of a physical model includes the selection of tunnel
bricks and their bond pattern, dimensions, restrained boundary conditions.
Figure 3.1 Original and half-scale Mellowed red stock bricks
The small-scale brick-lined physical tunnel model designed and constructed was
subject to spatial limitations in the laboratory. The small-scale modelling of masonry
structures such as masonry arch bridges has been proved to be a reliable solution by
Davies et al (1998) and Alonso (2001).
In this investigation, bricks used in constructing the physical models were half-scale
(see Figure 3.1). Namely, they were half the size of a full-size ‘Mellowed red stock
brick’ (see later in Section 3.3.1) and had dimensions of 107.5 × 51.25 × 32.5 mm (L
× W × H). Thus the dimension of the brick-lined tunnel profile was designed to be
690 × 887.5 mm (L × H), shown in Figure 3.2.
69
3.3.2 Brick bond pattern
Figure 3.2 Front view of the brickwork liner
The tunnel’s brick lining, having the profile of a horseshoe was built with the aid of
a wood arch support. As shown in Figure 3.2, the tunnel consists of three layers of
bricks situated at the arched region with each layer having bricks of similar size. The
sidewalls, on the other hand, comprise one and a half bricks juxtaposed to each other
but layered alternately. Each brick piece was separated by a 5 mm mortar joint. The
tunnel was not constructed with any wedge-shaped bespoke bricks, in line with the
construction pattern of many existing ancient brick-lined tunnels.
Although various brick bond patterns are used in reality for tunnel construction (see
Section 2.4.2 in details), for consistency this research utilised the stretcher bond
along the width of the entire tunnel.
3.3.3 Rigid box
A rigid support fashioned mainly from wood was utilised to support the soil
surrounding the brick liner and to behave like a boundary restriction. The support
3rd
ring
st
ring
2nd
ring
0 mm
.5 mm
70
was in the form of a box of the dimensions shown in Figure 3.3, and with the
exposed faces of the second and the third ring of the brickwork tunnel covered with
Perspex. It can be seen from Figure 3.3, brick liner is placed into the box (see
Section 3.2 and 3.5 for more details).
Figure 3.3 The rigid box surrounding the brick-lined tunnel
3.4 Physical model materials
Three specified materials may largely influence the structural strength and
mechanical behaviour during the tests, i.e. brick, mortar, and surrounding soil. The
details of each material are shown.
3.4.1 Brick
In accordance to the ancient masonry arch bridge tested by Hogg (1997) and Alonso
(200 ), ‘Mellowed red stock brick’ sourced from Wienerberger Ltd. was utilised for
physical models tested in this investigation. Technical details of the bricks are shown
in Table 3.2.
* Unit: mm
Yellow: Wood board Green: Perspex
covering the outer
two layers of
brickworks Light red: Inner
layer of brickworks
71
Table 3.2 Technical details of the brick (Alonso, 2001)
3.4.2 Mortar
The mortar mix utilised comprised High strength Portland cement, hydrated lime and
sand. While the cement and lime conformed to British standard specifications, BS
EN 197-1-CEMI 52.5N and BS EN 459-1:200, the red builder’s sand supplied was
determined to be poorly graded. This was found when a representative sample of the
sand material was sieved in accordance to BS 1377-2:1990. The proportions of the
different particle sizes are shown in Table 3.3 and the particle size distribution is
illustrated in Figure 3.4.
Figure 3.4 Particle size distribution (PSD) of red builder’s sand
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
Per
cen
tage
pass
ing
Particle size (mm)
Brick name Mellowed red sovereign stock
Brick type Solid fired clay - facing brick
Standard work size 215 × 102.5 × 65 mm
Dry weight 2.5 kg (typically)
Appearance A stock of oranges and red shades
Minimum compressive strength >21 N/mm2
72
Table 3.3 Grading data for mortar sand
3.4.3 Surrounding soil
Being a vital part of the physical tunnel model, the surrounding soil such as
overburden soil cannot be neglected. In this study, this is represented by a compacted
poorly graded Portaway sand (normal building sand), which was not subjected to any
hydrostatic effects throughout the testing programme.
The sand’s relative particle proportions and PSD was determined as prescribed by
BS 1377-2:1990 and is shown in Table 3.4 and Figure 3.5 respectively.
BS Sieve Size % Passing by Mass
6.3 mm 100
5 mm 99.8
3.35 mm 98.9
2 mm 97.9
1.18 mm 97.1
600 µm 94
425 µm 76
300 µm 25.8
212 µm 9.4
150 µm 3.6
63 µm 0.4
73
Table 3.4 Grading data for surrounding soil
Figure 3.5 Particle size distribution chart of surrounding soil
3.5 Model construction and loading process
All the physical models investigated in this study followed an identical construction
process to ensure consistency and comparability. The key elements of the
0
20
40
60
80
100
0.01 0.1 1 10
Per
cen
tage
pass
ing
Particle size (mm)
BS Sieve Size % Passing by Mass
5 mm 100
3.35 mm 98.6
2 mm 85.6
1.18 mm 72.5
600 µm 50.2
425 µm 29.4
300 µm 11.8
212 µm 6.2
150 µm 3.5
63 µm 0.4
74
construction process were the brickwork liner, rigid box, plastic sheeting, and
surrounding soil.
3.5.1 Construction of brickwork liner
The bricks used to construct the liner comprised approximately 500 bricks of half-
scale bricks and ‘half bat’ (see Table 3.5 for details) cut beforehand by electrical saw.
The fabrication process commenced with the construction of two symmetrical
sidewalls comprising 10 layers separated by 5 mm mortar joints to prevent
asymmetrical loading of the structure. The sidewalls were followed by the arch
which comprised three layers of brickwork formed with the assistance of the wood
arch support (see Figure 3.6 (a)). To separate the brickwork from the wooden
support, a polythene sheet was placed at the interface of the brickwork and the
wooden support, and was removed later when the mortar had sufficiently cured.
Figure 3.6 (a) Building process with wood arch support; (b) The small-scale
brickwork liner of the tunnel
The stretcher bond pattern of the tunnel arch was formed using 50 half-scale bricks
cut into half as ‘half bat’ and installed to form the 3 consecutive arch rings. The first,
75
second, and third arch rings required 30, 32 and 34 courses of bricks respectively to
complete, as can be seen in Figure 3.6 (b).
Table 3.5 Dimensions of bricks used in the construction
Half bat*: A brick cut in half across its length.
Although it was supposed to maintain a 5 mm mortar joint thickness it varied
between 4 mm and 10 mm due to the geometric limitations to the formation of the
brickwork at the tunnel arch. In addition, workmanship error was made especially
when building the arch and towards the crown. The outer side of the arch went up to
12 mm at some points.
In total, it took 7 working days to finish the first brick-lined tunnel, around 56 hours
together. Then, the wood arch support was taken out after 7 days and the tunnel
became self-supporting.
After the removal of the wood support, repointing work was done especially
underneath the arch and at the sidewalls with the same proportion of mortar mix to
prevent any crack generation or defect. A minimum of 28 days curing period was
considered while the accomplishment of the rigid box could be done.
Scale Length (mm) Width (mm) Depth (mm)
Original 215 102.5 65
Half 107.5 51.25 32.5
Half bat* 53.75 51.25 32.5
76
3.5.2 Rigid box
The wood board and Perspex were cut following the design size and sealed with
clear silicone sealant. In addition, several steel angles were fixed at each box edge to
strengthen the box.
After a full analysis of potential loads, deflections and factors of safety, a set of hot
finished square and rectangular hollow section steel beams were designed and bolted
at the front and back of the box. It consisted of six short hollow beams and one long
hollow beam at each face (see Figure 3.7). Details of the hollow beams are in Table
3.6. The hollow beams were connected with steel packing of 50 mm thickness,
bolted with steelrods (Φ 25 mm). They worked effectively to increase the stiffness of
the box.
An additional set of wood wedges was at the position of 1/3 and 2/3 of the long
beam against ‘A’ framesbolted on the robust floor, which supported and increased
the bending capacity of the long beams (see Figure 3.8).
The two sides of the box were also be strengthened against the loading frame by
wood wedges.
77
Figure 3.7 The rigid box of the first physical model
Figure 3.8 Wood wedges on the long beams against ‘A’ frames
78
Table 3.6 Dimension of hollow section beams
3.5.3 Plastic sheeting
To avoid the surrounding soil slipping out of the box through the Perspex and
brickwork gap up to 2 mm while loading, the tunnel was covered with white plastic
sheeting all around the rigid box (see Figure 3.7) before filling the surrounding soil.
Moreover, plastic sheeting played an important role in reducing the friction between
the soil and the box when loading occurred.
3.5.4 Surrounding soil
The placement of the fill sand commenced just before the loading test as it
represented a heavy dead load. The Portaway sand was placed and compacted in
layers. Each layer was approximately 125 mm thick with a standard 2.5 kg
compaction test drop hammer for 20 times, up to 1075 mm depth from the box
bottom. Care was taken during surrounding sand compaction, especially close to the
tunnel arch where the fill was less.
The density of 1832 kg/m3
(see Section 4.2.4 for details) and the depth of 1075 mm
for surrounding soil from the tunnel toe were kept the same for all physical model
tests.
Dimension NO. 1 NO. 2 & 3 NO. 4 & 5 NO. 6 & 7
B (mm) 200 150 200 150
D (mm) 200 250 200 150
t (mm) 12 16 10 8.8
Length (mm) 2800 1220 1130 1000
79
3.5.5 Loading system installation
1) Uniform load
Monotonic (Static) load tests were run through the research. For these tests, load
equipment consisted of one loading frame and a long cross beam to hang two hand-
operated ‘Enerpac’ jacking systems associated with two load cells (Capacity was 500
kN each), to properly distribute the point load on top of the model and measure the
imposed load. The load capacity of one hadraulic jack was 1000 kN and the
maximum movement was 150 mm. (see Figure 3.9)
The load from two jacks was applied evenly on the whole surface of the overburden
soil by a load spreader beam (1690 × 150 × 250 mm, L × W × H) with 5 point
loading rollers (equally distributed along the length of the box), and a 20 mm thick
steel plate of 1950 mm long and 300 mm wide underneath, as can be seen in Figure
3.10.
Figure 3.9 Loading system installation for uniform load
80
Figure 3.10 Load distribution design from two jacking systems
2) Concentrated load
Figure 3.11 Concentrated load jacking system
For the concentrated load test, the same loading system was used with one hand-
operated jack and one load cell (Capacity was 1000 kN) to distribute the point load
by a 30 mm thick steel plate of 330 mm wide and 300 mm long, on the surface of the
overburden soil just above the tunnel crown. The hydraulic jack was the same as
uniform load test with 1000 kN capacity and 150 mm maximum movement. (see
Figure 3.11 and Figure 3.12)
81
Once a test was completed, the brick-lined tunnel was demolished and the Portaway
sand was removed. The rigid box and wood arch support were cleared and made
ready for the next model building. The duration for each physical model test from
construction, mortar curing, loading to demolition was around 7 weeks.
Figure 3.12 Loading system installation for concentrated load
3.5.6 Loading procedures
Loading from 0 kN was initiated using hand pumps connected to hydraulic jacks and
load increments of 40 kN were maintained for the majority of the time for each test.
As the load accumulated on the structure and the failure load was imminent, the load
interval was reduced to 10 kN until the structure failed at its ultimate load. It would
be seen from the instantaneous recorded data of potentiometers (details in Section
3.7) shown on the monitor screen that the load versus crown displacement curve
started to behave from linear to non-linear, which is a symbol of upcoming structural
failure.
82
In most instances, load increments were sustained for one to two minutes to allow
for logging of potentiometer data, the capture of digital photos and the laser scanning.
Photogrammetry undertaken in the between load increments involved capturing
images at different positions in both ‘portrait’ and ‘landscape’ orientations.
3.6 Tunnel monitoring instrumentation
It is imperative in any tunnel examination to monitor tunnel distortions/deformations
in addition to other physical defects in the entire tunnel shell, such as leaks, cracks,
and corrosion. Traditionally, this has been achieved with the use of physical-contact
techniques such as steel tapes and tape extensometers. More recently, however
highly precise and non-intrusive methods have been employed to achieve the
aforementioned purpose. Both the traditional and modern methods of monitoring
were utilised in this investigation and are the subject of discussion in the
forthcoming section.
3.6.1 Advanced monitoring techniques
Due to the limitations of traditional monitoring methods (details in Section 2.3), two
advanced, non-intrusive techniques, namely the laser scanning and photogrammetry
were used to monitor the distortion and ascertain the evolution of defects on the
tunnel shells in this study. The calculation methods used in analysing the outputs of
both techniques were similar to each other. The sections below introduce the
instrumentation of the advanced techniques.
83
1) Laser scanner
The FARO Focus3D
, a light and user-friendly laser scanner was used for monitoring
work (see Figure 3.13). It was relatively a very small 3D scanner, with a size of only
240 × 200 × 100 mm and a body weight of 5 kg. This laser scanner has a touch
screen to control all scanning functions and is extremely easy to use. The scanning
process takes only a few minutes, saving up to 50% of scan time compared to other
scanners. The laser scanning process required no special preparation prior to the start
and the scan.
Figure 3.13 The front view of the laser scanner FARO Focus3D
(Faro Ltd., 2011)
Table 3.7 below displays more technical specifications. (Faro Ltd., 2011)
Table 3.7 Technical specifications of the laser scanner
Main Features The Laser Scanner FARO Focus3D
Measurement Range 0.6 m - 120 m
Vertical field of view 305°
Horizontal field of view 360°
Max. vertical scan speed 97 Hz
Ambient temperature 5° - 40° C
84
The physical model was scanned after each load increment and a 3D image obtained
by assembling the millions of ‘clouds of points’ with coordinates. Via post-
processing work of the point cloud data, it was possible to determine the extent of
deformation at specific locations on the tunnel structure. Details of the post-
processing work and subsequent results are illustrated later in Section 3.9.
2) Digital camera
For the photogrammetry work, a Canon EOS-5D Mark Ⅱ Digital SLR camera was
used for image recording during the loading tests (see Figure 3.14).
Prior to loading, preparation for photogrammetry required the placement of around
150 reflective markers on the structure. These were stuck to the first lining ring
(intrados) at both tunnel openings, to serve as reference points to monitor
deformation variations during the tests. Additionally, it ensured that the ambient
lighting was sufficient for the process.
Figure 3.14 The top view and the front view of Canon EOS-5D Mark Ⅱ
(Imaging Resource, Ltd., 2009)
85
3.6.2 Potentiometer
The purpose of using potentiometers was to compare their outputs to results from
monitoring using the digital camera and the laser scanner. Linear potentiometers
were positioned at specific monitoring points on the tunnels’ crowns, springing and
toes, during the monotonic loading tests to measure horizontal and vertical deflection.
With regards to the potentiometer installations, ten light aluminium targets were
attached to the specific monitoring positions (crown, springing, and toes) on the first
lining ring of the tunnel faces. These targets provide a reactive force to horizontal
and vertical potentiometers. Here crown refers to the highest point of an arch layer of
the tunnel liner, springing is the level where an arch or vault rises from a support,
and toe is the bottom region of the horseshoe tunnel (see Figure 3.15).
Figure 3.15 Five monitoring points in yellow at each tunnel face
Of the ten linear potentiometers employed, eight had a 30 mm range (see Figure 3.16)
and the remaining two mounted on the tunnel crown, a range of 50 mm.
Springing point
rown point
Toe point
86
Figure 3.16 Potentiometer with 30 mm range
3.7 Test results of the first and the second models under uniform load
Results from the mechanical testing of the first and second physical models were
compared to ascertain the relative effects of the different mortar mix proportions
used in the construction of their brick linings. The data obtained proved useful for
establishing typical behavioural characteristics for a uniformly loaded tunnel and
determining specific tunnel failure criterion. Furthermore, the outputs of the
mechanical tests were relevant as reference points for the numerical validation that
ensued.
3.7.1 Ultimate load capacity and tunnel mode of failure
Figure 3.17 shows the transmitting path of the uniform load from the steel plate on
top of the overburden soil to the tunnel. In this figure, H was the soil depth from the
surface to the tunnel’s toe, h was the soil depth above the tunnel crown, q was the
uniformly distributed load acting on the tunnel arch and e was the horizontal stress
acting on the tunnel, from the top to the bottom of the tunnel (e1 to e2). By virtue of
its shape, the uniformly distributed load on the arch of the tunnel caused the tunnel to
fact as a monolith thereby forcing the applied load to be transmitted to the sidewalls,
which led to the shear failure on the tunnel sidewalls as the primary mode of failure.
87
Figure 3.17 Tunnel model of failure under uniform load
The first physical model failed at a load of 995 kN, corresponding to a pressure of
1.49 MPa. The major shear failure was observed on the two sidewalls together with
evidence of minor tensile failure on the tunnel’s crown. Although a similar failure
pattern was observed in the second physical model test, the model’s ultimate load at
failure was found to be 69.7% of that of the first model, having failed at 694 kN (or
equivalent pressure of 1.04 MPa). The test data from these two uniform load tests on
the physical models are shown in Table 3.8.
Table 3.8 Outputs from uniform load tests
Physical
model
Mortar mix
proportion
Failure
load
Mode of failure Location of failure
1 1:1:6 (higher
strength)
995 kN Mainly shear failure,
partially tensile
failure
Mainly tunnel
sidewalls, partially
tunnel arch
2 1:2:9 (lower
strength)
694 kN Mainly shear failure,
partially tensile
failure
Mainly tunnel
sidewalls, partially
tunnel arch
88
The result is consistent with the comparatively higher compressive strength of the
brickwork in the first physical model (More details are shown in Chapter 4). It also
suggests a correlation between compressive strength of constituent brickwork and
the tunnels’ ultimate load capacities, in that the tunnel comprising brickwork of
higher strength failed later than its counterpart when both were subject to identical
load regimes. The result is consistent with previous research by Hogg (1997), the
first physical model could withstand a larger uniform load than the second physical
model, possibly because it comprised brickwork of higher compressive strength.
3.7.2 Deflection behaviour
It is shown in Figure 3.18 that the tunnel under uniform load deforms inwards with
the tunnel arch transferring the imposed uniform load downwards to the sidewalls,
resulting in a crushing phenomenon near the arch springing (see Figure 3.22 (b)).
Figure 3.18 Deformation tendency of the tunnel under uniform load
From averaged outputs of the two vertical linear potentiometers located midpoint of
the tunnel’s crown and the eight potentiometers at the springing and toes of two
tunnel faces, the pressure-deflection curves shown in Figure 3.19 and Figure 3.20
were produced for the tunnel’s crown and the springing.
89
The pressure-crown deflection relationship in Figure 3.19 presents similar arch
structural stiffness of the two brick-lined tunnels. It suggests that the stiffness of the
brickworks, such as Young’s modulus of the brickworks, does not have significant
effect on the brick-lined tunnels, which is consistent with the parametric study of
numerical simulations in Chapter 4. However, the first physical model test with
comparatively stronger ultimate load capacity corresponded with more deformation
(62.3 mm) at failure, while the crown displacement at failure of the second physical
model test was 46.2 mm as 67.6% of that of the former test.
It is observed from Figure 3.20 that the springing structural stiffness of the second
physical model reduced to around 3/4 of that of the first physical model. It indicated
that the brickwork stiffness of the second model had a great influence on the
springing structural stiffness when the lateral load from the surrounding soil was
parallel to the bed joints (horizontal joint in masonry).
The smaller development of the springing deformation at the same load level in the
first physical model test implied that the springing of the tunnel arch connected to
the sidewall started to crush early than that in the second physical model test, which
slowed down the movement of the springing.
90
Figure 3.19 Pressure-crown displacement (vertically) curves under uniform
load
Figure 3.20 Pressure-springing displacement (horizontally) curves under
uniform load
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown displacement (mm)
Physical model test 1
Physical model test 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25
Pre
ssu
re (
MP
a)
Springing displacement (mm)
Physical model test 1
Physical model test 2
91
3.7.3 Cracking behaviour
Initiation of radial and stepped cracking was observed in the outwardly facing mortar
joints of the first, second and third arch rings during the process of loading. These
were noted to occur at 59% (594 kN) and 56% (392 kN) of the total loading regime
for the first and the second physical models respectively.
As the loading progressed, the cracks were noted to propagate at the intrados of the
tunnel arch (i.e. the inner surface of the tunnel arch). Subsequently, an increase in
growth of radial cracking at the intrados of the tunnel arch was observed (see Figure
3.21).
Additionally, the onset of diagonal cracking cutting through the two tunnel sidewalls
and leading to imminent shear failure was observed as evidenced by Figure 3.22.
Figure 3.21 Crack failure under uniform load
92
Figure 3.22 (a) Shear failure at sidewalls; (b) Crushing phenomenon at the arch
springing
3.8 Test results of the third model under concentrated load
The third physical model was subjected to concentrated loading above the centre of
the tunnel crown. The mortar of the same mix proportion (1:2:9) as per the second
physical model was used in the construction of the third physical model.
Consequently, it was possible to compare the mechanical behaviour of the tunnel
structures subjected to two different load types i.e. the second physical model under
uniform load and the third physical model under concentrated load.
3.8.1 Ultimate capacity and tunnel mode of failure
Figure 3.23 illustrates the third physical model under concentrated load acting on the
overburden soil area just above the tunnel crown, transmitted by a steel plate
(loading area of 330 × 300 mm, mentioned in Section 3.5.5), where f was the
distributed load acting on the centre of the tunnel arch. The failure was due to the
development of five structural hinges namely point A to E at the tunnel arch,
93
occurring since the tunnel arch was subjected to symmetrically distributed loading,
which showed an agreement with Page (1993). Theoretically the five structural
hinges would appeared at certain position of the tunnel (i.e. 1/6, 2/6, 3/6, 4/6, 5/6
section of the tunnel arch) as shown in Figure 3.23.
Figure 3.23 Tunnel model of failure under concentrated load
The third physical model experienced a sudden failure at 73 kN, corresponding to the
failure pressure of 0.73 MPa on the loading area of 330 × 300 mm which was 70%
of the failure pressure of the second physical model test (see Table 3.9). During
loading, a five-hinge failure mechanism was observed as shown in Figure 3.24
specially appeared at the second and third rings of the tunnel arch with hinge points
A, B, D and E, and through three arch rings with hinge point C. In addition, the
collapse of partial ring sections due to ring separation of three arch rings at the
tunnel crown, occurred suddenly at the maximum load as can be seen in Figure 3.24.
The ring separation would normally occur in a multi-ring masonry arch subjected to
94
loading (Chen, 2007). The test data from the concentrated load test on the third
physical model is shown in Table 3.10.
Figure 3.24 Collapse during the physical model test under concentrated load
Table 3.9 Loading outputs from three physical models
Table 3.10 Outputs from the concentrated load test
Physical model Loading style Failure load Loading area Failure pressure
1 Uniform load 995 kN 0.67 m2 1.49 MPa
2 Uniform load 694 kN 0.67 m2 1.04 MPa
3 Concentrated load 73 kN 0.10 m2 0.73 MPa
Physical
model
Mortar mix
proportion
Failure
load
Mode of failure Location of
failure
3 1:2:9 (lower
strength)
73 kN Mainly five structural hinges,
collapsed due to ring
separation
Mainly
tunnel arch
95
3.8.2 Deflection behaviour
The deformation trend of the tunnel under concentrated load differed from that under
uniform load. The simplistic depiction of the deformation tendency to failure in
Figure 3.25 shows the sidewalls as having deformed outwards from the original
tunnel profile and the crown at the third ring inwards over the loading period. Figure
3.23 specifically illustrates the deformation tendency to failure in red with structural
hinges at the tunnel arch, which separated the tunnel into six sections.
Figure 3.25 Deformation tendency of the tunnel profile under concentrated load
For the same mortar mix ratio of 1:2:9, the third physical model under concentrated
load experienced only half vertical movement of the crown at failure, compared to
that of the second physical model under uniform load shown in Figure 3.26. Because
in the third physical model, the tunnel crown recorded at the first (inner) arch ring
deformed diagonally, developing a structural hinge at the third (outer) arch ring and
cracks through three arch rings at the tunnel crown (see Figure 3.23), while in the
second physical model, the tunnel crown only moved vertically.
96
With regards to springing deflection at failure, the third physical model had
comparable springing displacement within 5% difference from that of the second
physical model as can be seen in Figure 3.27.
Figure 3.26 Pressure-crown displacement curves under uniform and
concentrated load
Figure 3.27 Pressure-springing displacement curves under uniform and
concentrated load
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50
Pre
ssu
re (
MP
a)
Vertical crown displacement (mm)
Physical model test 2
Physical model test 3
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30
Pre
ssu
re (
MP
a)
Springing displacement (mm)
Physical model test 2
Physical model test 3
97
3.8.3 Cracking behaviour
During the concentrated loading of the third physical model, the formation of
structural hinges with cracking was noted at 62% of the loading programme (i.e. load
of 45 kN, pressure of 453 kPa). Figure 3.28 shows the major structural hinge with
cracking at the tunnel crown whist Figure 3.29 illustrates the five structural hinges as
points A to E and cracking development, which were almost symmetrical in the
experiment. Furthermore, two springings initiated minor cracks with the potential to
develop into structural hinges.
At failure, ring separation with radial cracking occurred among three arch rings at
the tunnel crown, which led to collapse of partial tunnel section.
Figure 3.28 Structural hinge at tunnel crown along the width under
concentrated load
98
Figure 3.29 Structural hinges with cracking of the tunnel arch under
concentrated load
3.9 Post-processing work of advanced monitoring techniques
3.9.1 General introduction
During the loading tests, two advanced techniques (i.e. photogrammetry and the laser
scanning system) were used for monitoring tunnel shell distortions and inspecting
defects. The raw data from the techniques utilised was post-processed using the
commercial software, ‘Australis’ and ‘Geomagic Studio 10’ for close-range digital
photogrammetry and the laser scanning system respectively. The implementation and
output of the techniques with regards to this study are shown in the following
sections.
3.9.2 Tunnel monitoring and data processing of measurements using
photogrammetry
Australis (Version 7.0) is used to make 3D measurements of numerous targeted
points on an object of interest, which in the instance of this investigation are physical
99
models of tunnels. The targets for measurement points usually comprise retro-
reflective dots stuck on the object. Additionally, distinct and retro-reflective coded
targets against a dark background are placed nearby the object of interest, to
facilitate the automatic measurement, as shown in Figure 3.30.
Figure 3.30 Dots and coded targets in green
The Australis Users’ Guide prescribes a process involving measurements, scale
setting, coordinate system transformation and exporting points of interest, for
successful analysis of photogrammetry raw data.
a) Project set up and manual measurements
Following the guide, a project comprising selected images obtained at the same
loading stage but from different image stations was set up. Full measurements
(conducted manually) were then made, ensuring that every targeted point appearing
in at least two images were matched. Via this process, a 3D photogrammetric
100
network comprising multiple tunnel images and object points obtained from specific
camera stations could be formed and measured.
In Figure 3.31 for example, thumbnails and expanded versions of images obtained
from different stations are shown, along with a 3D tunnel point profile of both tunnel
openings (shown in green at the right bottom). However, the object of interest i.e.
brick-lined tunnel was not scaled in accordance with the real scale at this stage.
Figure 3.31 3D photogrammetric network of multiple images and the 3D view
101
b) Setting the scale
In this step, the tunnel measurements were scaled to true size using a scale bar. The
process utilises the image of a scale bar of known distance between its two end
targets. The scale bar targets are measured and a scale factor is computed and
applied. With this registered value, subsequent tunnel point-to-point distances were
made in reference to it.
c) Coordinate system transformation using control points
As the 3D images obtained for the tunnels at each load were initially set up in their
own local coordinate systems, it was necessary to undertake coordinate
transformation to a single Primary Coordinate System. In this study, the coordinate
system of the tunnels’ original 3D images (without any load) was utilised as the
Primary Coordinate System.
The transformation is defined by ‘control points’ with known coordinates in two
Cartesian reference systems: Xc, Yc, Zc coordinates from the existing Primary
Coordinate system, and X, Y, Z coordinates from the Secondary Coordinate system.
Figure 3.32 illustrates a 2D coordinate transformation, which is similar to 3D
transformation.
Given three or more control points that are non co-linear (as Points 2, 10, 11 and 15
here), a 2D transformation can be performed from the specified Secondary XYZ
system to the Primary XcYcZc system of the control points.
d) Exporting XcYcZc coordinate points of interest
Finally, the XcYcZc coordinate data is exported for further analysis in Excel.
102
Figure 3.32 2D transformation of XY coordinates into Xc, Yc coordinates (after
Australis Users’ Guide)
b) Measured points in
Secondary X, Y system
a) Control points in Primary Xc,Yc
system (Points 2,10,11 and 15)
c) Measured points transformed
into the Primary Xc, Yc system
103
3.9.3 Tunnel monitoring and data processing of measurements using the Laser
Scanning Technique
‘Geomagic Studio 10’ software is used to post-process the test data for the close-
range laser scanner measurements.
The scanning object exists in ‘Point phase’ in Geomagic Studio as a collection of
scanned points. The Point phase explains the registration and merging of two
adjacent points to form a polygon object. The basic workflows of point phase are
shown below, taking the scanning of failed physical model after concentrated load as
an example:
a) Deleting redundant points and reducing noises
Since the raw data from scanning is of 360 degree, there are a large number of
unnecessary points. It is essential to delete unrelated points to minimise the amount
of data. After that, ‘clouds of points’ 3D model of brick-lined tunnel are obtained
shown in Figure 3.33.
Some of the redundant points nearby the point cloud tunnel may remain, which are
hard to be reduced manually. Those so-called noises could produce sharp edges, or
cause smooth curves to become rough when a polygon object is created. Thus, Noise
Reduction function is used to reduce the number of errant points, resulting in more
uniform arrangement that the polygon object can be formed more smoothly.
104
Figure 3.33 Partial 3D model in point clouds
Figure 3.34 3D tunnel model after wrapping
105
b) Wrapping the tunnel model
Using the Wrap function to create a polygon object: Wrapping performs as stretching
plastic sheeting around one point and pulling it to form a polygonal surface, thus
changing the 3D model of point clouds into a polygonal object with sided edges as
shown in Figure 3.34.
c) Observation for cracks and defects
Figure 3.34 clearly demonstrates the mode of failure and hinges appearing at the arch,
from the front view and side views of the scanning model. Even the layout of the
brickwork could be seen especially at two sides of the tunnel’s inner surface.
d) Distance measurement
Now the original point cloud has become a polygon object, which could be measured
using distance measurement. Since several cracks and defects have been observed, it
is required to measure the crack width and length (see Figure 3.35). This allows the
laser scanning technique to be compared to the conventional vernier calliper.
e) Deformation measurement and Mapping of the differences
An average value for each deformation is determined by analysing the registered
point cloud in coordinates.
3D Compare function helps to generate a 3D colour coded mapping of the
deformations between two surfaces at different conditions, such as under various
loadings. More figures illustrated this function are shown in Appendix B.
106
Figure 3.35 Crack width and length measurement
3.9.4 Results and comparison of the monitoring equipment
1) Introduction to measurement comparisons
In order to compare the tunnel crown deformation measuring results of the
monitoring equipment (photogrammetry, the laser scanning system and
potentiometers), physical model test 1 with a mortar mix proportion of 1:1:6, was
used here as an example, at the uniform load of 0 kN and 590 kN.
To compare the distance measuring results (crack width and length) of the
monitoring equipment (photogrammetry, the laser scanning system and the vernier
calliper), physical model 3 (with a mortar mix proportion of 1:2:9) at failure under
concentrated loading, was employed.
2) Deformation measurement by photogrammetry
Through photogrammetry, it was possible to determine deformations at other
targeted points of interest, such as those located at a quarter and three quarters of the
Length
(b) Width
107
span of the tunnels’ arches, except the crown deformations of tunnels. They were
also important points to monitor the arch behaviour (see Figure 3.36). The centre
point of all the target points was maintained using the Centroiding function in
Australis for the different loading conditions as seen in Figure 3.37.
For the tunnel of the physical model 1 with a mortar mix proportion of 1:1:6 under
the uniform load of 0 kN and 590 kN, vertical crown deformation and diagonal
deformation at the target points located at a quarter span of the tunnel arch, have
been analysed as shown by the coordinates presented in Table 3.11.
With the help of photogrammetry, the pressure versus displacement curve at a
quarter span of the tunnel arch from load 0 kN to 590 kN is shown in Figure 3.38. It
would be compared with numerical results in Chapter 4.
The starting point of the coordinate system was set to the first camera station as
default.
Figure 3.36 Target points in yellow measured via photogrammetry
108
Figure 3.37 Target points used for photogrammetry processing
Table 3.11 Deformation results by photogrammetry
Target point at the crown
Position No. Coordinates from two measurement epochs
Deformation
(mm) X (mm) Y (mm) Z (mm)
A (at 0 kN) -53.09 1058.14 239.79 35.63
A’’ (at 590 kN) -52.06 1068.80 205.80
Target point at the a quarter span of the tunnel arch
Position No. Coordinates from two measurement epochs
Deformation
(mm) X (mm) Y (mm) Z (mm)
B (at 0 kN ) -300.00 1064.75 97.10 20.78
B’’ (at 590 kN) -314.54 1052.94 88.11
109
Figure 3.38 A quarter span displacement curve with the aid of photogrammetry
3) Deformation measurement by the laser scanning system
Figure 3.39 and Figure 3.40 demonstrate the 3D deviation of the tunnel crown part in
different colours, showing the displacement between images at 0 kN and 551 kN
load. The maximum deformation was at the crown around 30 mm. The deformation
gradually reduced towards the springing of around a minimum of 2 mm.
The blank parts in the images were due to the covering of the steel bars bolted on the
hollow steel beam when scanning. The grey parts were as a result of insufficient data
for valid comparison, from the test against the original object. We could also see
from Appendix B for more details, the 3D deviation between each two scanning
image at different loads.
An average value from three points at the crown was recorded for load 0 kN and 590
kN, shown in Table 3.12. The result was compared with the results of both
photogrammetry and potentiometers in the later section, for the same physical model
test.
0
0.2
0.4
0.6
0.8
1
0 10 20 30
Pre
ssu
re (
MP
a)
One quarter disp (mm)
One quarter displacement curve
Photogrammetry
110
Figure 3.39 The side view of the 3D deviation of the tunnel crown
Figure 3.40 The oblique view of the 3D deviation of the tunnel crown
111
Table 3.12 Deformation results by the laser scanning technique
4) Distance measurement by photogrammetry
The accuracy of distance measurement by photogrammetry, such as the crack width
and length, is of great importance to be figured out for the monitoring work.
Figure 3.41 and Figure 3.42 show the major crack (hinge failure) at one third of the
tunnel arch of the physical model 3. An average crack length of three values has
been taken; while crack width has been specified and measured from three different
locations due to width variations along the crack (the beginning of the crack, the
middle of the crack and the end of the crack, position numbered 1 to 3 separately) in
Table 3.13. One of the key influence factors would be the processing work of manual
measurement operation. For this tunnel arch, the estimated accuracy of 3D point
coordinates was shown in Table 3.14, with the overall accuracy of ± 0.45 mm.
Position No.
Crown coordinates from two measurement
epochs Deformation
(mm) X (m) Y (m) Z (m)
1 (at 0 kN) -1.583638 -0.098053 0.535654
40.10
2 (at 0 kN) -1.582363 -0.108903 0.534358
3 (at 0 kN) -1.582369 -0.121182 0.536781
Average -1.582790 -0.109379 0.535598
’’ (at 5 0 kN) -1.575600 -0.092600 0.494900
2’’ (at 590 kN) -1.575600 -0.104300 0.495100
3’’ (at 590 kN) -1.578000 -0.116400 0.496100
Average -1.576400 -0.104433 0.495367
112
Figure 3.41 The major crack at one third of the tunnel arch of the physical
model 3 for the measurement of crack length and width
Figure 3.42 Non-targetted points of interest in coordinates along a major crack
Crack width No.1
Crack width No.2
Crack width No.3
The major crack
113
Table 3.13 The major crack results by photogrammetry
Table 3.14 Estimated accuracy of 3D point coordinates
5) Distance measurement by the laser scanning system
The same crack (hinge failure) at one third of the arch was measured using the laser
scanning technique, as that measured using photogrammetry, shown in Figure 3.43.
For crack length (i.e. total distance), average value was taken from three results. For
crack width, the beginning, middle and the end of the crack width were taken.
Results were shown in Table 3.15.
Crack length No. Crack length in each coordinate
Crack length
(mm) ΔX (mm) ΔY (mm) ΔZ (mm)
1 54.29 58.45 66.15 103.63
2 53.79 59.06 66.32 103.83
3 52.43 60.04 65.99 103.48
Average 53.50 59.18 66.15 103.65
Position No. Crack width in each coordinate
Crack width
(mm) ΔX (mm) ΔY (mm) ΔZ (mm)
1 (The beginning
position) 2.03 1.46 1.99 3.20
2 (The middle
position) 1.46 2.57 2.34 3.77
3 (The end
position) 0.63 1.26 1.35 1.80
X coordinate (mm) Y coordinate (mm) Z coordinate (mm) Overall (mm)
± 0.279 ± 0.673 ± 0.402 ± 0.450
114
Figure 3.43 Cloud points in coordinates among a major crack from the laser
scanning technique
Table 3.15 The major crack by the laser scanning technique
Crack length No. Crack length in each coordinate
Crack length
(mm) ΔX (mm) ΔY (mm) ΔZ (mm)
1 24.98 49.84 87.12 103.43
2 24.37 48.66 87.80 103.30
3 23.17 47.53 88.55 103.13
Average 24.17 48.68 87.82 103.29
Position No. Crack width in each coordinate
Crack width
(mm) ΔX (mm) ΔY (mm) ΔZ (mm)
1 (The beginning
position) 4.62 2.09 1.94 5.43
2 (The middle
position) 2.44 4.03 2.88 5.52
3 (The end
position) 1.78 1.97 0.86 2.79
115
6) Comparison results
Deformation measurement comparison
The crown deformation measurements from the potentiometers, photogrammetry and
the laser scanning system were compared using physical model test 1 with mortar
mix proportion 1:1:6, at the uniform load of 0 kN and 590 kN.
Ideally, the measuring method (i.e. potentiometers, photogrammetry and the laser
scanning technique) was in the same condition. However, the monitoring work
during loading was not simultaneous. During each loading interval, the results of
potentiometers were recorded first within 3 seconds, followed by digital images
taken for photogrammetry in 30 seconds and finally the scanning work of the laser
scanner that took around 1 minute.
During this minute, the tunnel may deform slightly to achieve equilibrium, thus there
were some variation in the deformation due to the small time difference in
measurement.
As Table 3.16 displays, the results difference between potentiometers and
photogrammetry was 8.5 mm while difference between potentiometers and the laser
scanner was up to 13 mm. For a shorter length of time between photogrammetry and
the laser scanner, the variation was smaller at 4.5 mm.
116
Table 3.16 Deformation results comparison at the crown
Distance measurement comparison
The length and width of the major crack (hinge failure) at one third of the tunnel arch
(with mortar mix proportion 1:2:9) under concentrated loading were analysed using a
vernier calliper (shown in Table 3.17), photogrammetry and the laser scanning
technique.
The measuring results from the vernier calliper were used as a benchmark. The
beginning, middle and the end of the crack width were measured by the vernier
calliper corresponding to position number 1 to 3 in Table 3.17.
Since this crack was measured after hinge failure and up to a new equilibrium, there
should be no more variation of the crack size. In other words, the crack results would
not be affected by the sequence of measurement.
Measuring method
Crown coordinates from two
measurement epochs Average
deformation
(mm) X (mm) Y (mm) Z (mm)
POT N/A
27.14
N/A
Photogrammetry -53.09 1058.14 239.79
35.63
-52.06 1068.80 205.80
Laser scanning -1582.79 -109.38 535.60
40.10
-1576.40 -104.43 495.37
117
Table 3.17 The major crack results by a vernier calliper
The results comparison was shown in Table 3.18 and Table 3.19 below.
For crack length, the difference between the vernier calliper and photogrammetry
was only 0.25 mm while the difference between the vernier calliper and the laser
scanner was as small as 0.11 mm. It shows a good comparison from both
photogrammetry and the laser scanning techniques within 0.3 mm.
For crack width, the difference between the vernier calliper and photogrammetry at
the 3 same positions was only 0.93 mm, 0.56 mm and 0.98 mm while the difference
between the vernier calliper and the laser scanner was 1.30 mm, 1.19 mm and 0.01
mm at these 3 positions. Therefore, the photogrammetry result compared was better
than the laser scanning.
Crack length No. Crack length (mm)
1 103.34
2 103.65
3 103.22
Average 103.40
Position No. Crack width (mm)
1 (The beginning position) 4.13
2 (The middle position) 4.33
3 (The end position) 2.78
118
Table 3.18 The major crack length results comparison
Table 3.19 The major crack width results comparison
3.10 Summary
3.10.1 Design of different physical models
A set of physical models was designed and outlined to represent the brick-lined
railway tunnels under different mortar and loading conditions. Half-scale typical
bricks were used for building the tunnel. In addition, dimensions, building and
installation process, and model materials for the tests were described.
3.10.2 Programme of physical model testing
A programme of physical model tests was conducted which included two static
uniform load tests to failure by varying mortar strengths and one static concentrated
load test to collapse.
Measuring method
Average crack length in each coordinate Average crack
length (mm) ΔX (mm) ΔY (mm) ΔZ (mm)
Vernier calliper N/A N/A N/A 103.40
Photogrammetry 53.50 59.18 66.15 103.65
Laser scanning 24.17 48.68 87.82 103.29
Measuring method The beginning
position (mm)
The middle
position (mm)
The end
position (mm)
Vernier calliper 4.13 4.33 2.78
Photogrammetry 3.20 3.77 1.80
Laser scanning 5.43 5.52 2.79
119
The mode of failure of physical models under uniform and concentrated load
differed. The first two physical models, which were under uniform load, failed as a
result of shear failure at the sidewalls as the major force was transferred to the sides.
The third physical model, which was under concentrated load, failed due to the
formation of five structural hinges at the tunnel arch.
The physical model under concentrated load seemed to reduce the ultimate capacity
of the tunnel by approximately 30%, comparing with the model under uniform load.
For both first and second physical models under uniform load, built with different
mortar mix proportions of the brick-lined tunnels, ultimate capacity was affected by
the compressive strength of the tunnel materials.
In summary, the small-scale physical model tests clearly indicated the mechanical
behaviour of the brick-lined tunnel with various mortar strengths and under different
loadings. The ultimate load capacity and mode of failure were also determined and
compared with different models.
The results of three physical models were used to validate the numerical models built
in Chapter 4 Numerical Simulation. Details and comparisons of the results between
physical models and numerical models are to be found in Chapter 4.
3.10.3 Monitoring techniques
During the loading test, potentiometers and two advanced techniques,
photogrammetry and the laser scanning, have been used for monitoring the tunnel
deformation. Moreover, inspecting defects (cracks) on the tunnel shells were carried
out by the two advanced techniques.
120
The data was analysed in the post-processing work and some conclusions were
drawn as below:
a) Photogrammetry usually works with the help of daylight, or a lighting system in
a dark environment, whereas the laser scanning system performs well without
any aid of lighting to observe cracks and defects.
b) The observation of defects such as a major crack around 3 to 5 mm wide could
be clearly identified in the laser scanning data. The accuracy of the laser
scanning technique is within 1.3 mm when compared with the vernier calliper,
while the accuracy of photogrammetry is within 1.0 mm. Both of them are
suitable to measure the tunnel defects such as major cracks.
c) Photogrammetry shows a strong potential for measuring tunnel deformation with
high accuracy with the help of lighting (see a)). The centre point of target points
could be easily captured by Centroiding function in the related post-processing
software Australis, rather than ambiguous point cloud of the target points in the
laser scanning system.
121
CHAPTER 4 NUMERICAL SIMULATION
4.1 General introduction
Nowadays, numerical modelling has been increasingly used to assess the stability of
tunnels and underground caverns. However, an analysis of the mechanical behaviour
of existing brick-lined tunnels remains challenging due to the complex material
components.
In this research, numerical models are developed using FLAC (Finite Difference
Method) and UDEC (Distinct Element Method) programmes to simulate the
mechanical behaviour of physical models after loading which were tested in Chapter
3. In other words, physical model tests also act as a validation for numerical
simulations. Thus in the future research, these numerical models could be applied to
the field study and enable accurate predictions of the actual mechanical behaviour of
a masonry tunnel.
4.2 Programme of material testing
4.2.1 General introduction
Due to the uncertainty in the material property database, the selection of material
properties is usually one of the most difficult parts in numerical simulation (Jia,
2010).
A series of laboratory tests were carried out to obtain the properties of brick, mortar
and soil conventionally. The tests included uni-axial and single stage tri-axial
compressive strength tests, direct shear box tests and so on. The following data were
122
gained from these tests and have been included in Appendix A in this thesis. These
properties were used in the numerical simulation:
a) Density (ρ)
b) Young’s modulus (E)
c) Uni-axial compressive strength (σc)
d) Mohr-Coulomb strength properties (cohesion c and friction angle φ)
e) Tensile strength (Tr)
For the other uncertain properties, an appropriate selection of properties based upon
the available database or laboratory tests was conducted in parametric studies,
compared with the results from the related physical model tests.
4.2.2 Brick
1) Uni-axial compressive strength test (UCS test)
The brick cylinder samples for the UCS test were cored from full-sized bricks of the
same batch. The required dimension was 37 mm in diameter and 74 mm (twice of
the diameter) in height. Thus, four samples could be cored from one full-sized brick
(see Figure 4.1 (b) & (c)). The tests were conducted by a stiff testing machine in the
Nottingham Centre for Geomechanics (NCG) (see Figure 4.1 (a)).
123
Figure 4.1 (a) Stiff testing machine in NCG; (b) & (c) Brick samples
The uni-axial loading rate was 0.02 mm/s. Initially, four sample tests were carried
out. Five more sample tests then followed to obtain the average properties, especially
for brick density, ultimate compressive strength and Young’s modulus, as shown in
Table 4.1.
The load versus displacement curve is also shown Figure 4.2. In general, most
samples failed at an average of 28.4 kN around 0.27 mm displacement. However, the
load value of sample 8 and sample 9 seemed different from the other samples as their
failure load exceeded 40 kN. The higher strength of these two samples is due to the
nonuniformity of a single brick during manufacture process. It’s one of the natural
characteristic of bricks.
124
Table 4.1 UCS test list of bricks
Sample
Reference
Average
Length
Average
Diameter
Sample
Density
Failure
Load
Ultimate
Compressive
Strength
Young’s
Modulus
(mm) (mm) (g/cm
3) (kN) (MPa) (GPa)
Sample 01 74.18 37.02 1.67 27.9 25.9 6.8
Sample 02 74.21 36.99 1.66 24.2 22.5 5.8
Sample 03 74.09 37.01 1.66 21.8 20.3 5.7
Sample 04 74.07 36.98 1.66 23.7 22.1 7.0
Sample 05 73.01 37.39 1.65 22.7 20.6 5.9
Sample 06 72.01 37.47 1.67 23.4 21.2 6.5
Sample 07 74.01 37.41 1.66 25.9 23.5 7.2
Sample 08 74.01 37.48 1.82 44.2 40.1 11.6
Sample 09 73.94 37.44 1.75 41.8 38.0 10.5
Average 73.73 37.24 1.69 28.4 26.0 7.5
Standard
Deviation 0.74 0.23 0.06 8.49 7.6 2.1
125
Figure 4.2 Load against displacement of UCS brick property test
2) Tri-axial compressive strength test (σ2 = σ3)
The single stage tri-axial compressive strength tests were carried out using 12
cylinder samples (The same size as the uni-axial test sample) at a confining pressure
of around 1, 3, 5 and 10 MPa individually. For each confining pressure, the tri-axial
test was repeated three times.
The results of the ultimate compressive strength helped to obtain the brick properties
of cohesion and friction angle. The details are shown in Table 4.2. The axial stress
versus axial strain curve is also shown in Figure 4.3.
Figure 4.4 shows the average Mohr-Coulomb circles at different confining pressures.
Strength envelopes could be drawn between two circles. Thus, the maximum,
minimum and medium friction angle and the relative cohesion could be gained as
shown below by the strength envelopes. The result details of various Mohr-Coulomb
strength envelopes are listed in Table 4.3. In this research, the maximum and
0
10
20
30
40
50
0 0.1 0.2 0.3 0.4 0.5 0.6
Lo
ad
(k
N)
Displacement (mm)
Uni-Axial Compressive Strength Test
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
Sample 7
Sample 8
Sample 9
126
minimum friction angle and cohesion were omitted, the medium ones were chosen
for numerical simulation.
Table 4.2 Tri-axial test list of bricks
Sample
Reference
Average
Length
(mm)
Average
Diameter
(mm)
Confining
Pressure
(MPa)
Failure
Load
(kN)
Ultimate
Compressive
Strength
(MPa)
Average
Ultimate
Compressive
Strength
(MPa)
Sample 01 74.05 37.42 1.11 29.6 26.9
21.7 Sample 02 74.01 37.46 1.11 20.8 18.8
Sample 03 74.01 37.36 1.11 21.3 19.5
Sample 04 74.07 37.42 3.06 40.0 36.3
36.0 Sample 05 74.08 37.46 3.06 38.5 34.9
Sample 06 73.66 37.46 3.06 40.5 36.7
Sample 07 73.68 37.42 5.01 40.3 36.6
46.3 Sample 08 74.06 37.45 5.00 65.4 59.4
Sample 09 74.01 37.46 5.01 47.1 42.8
Sample 10 73.98 37.45 9.93 76.8 69.7
69.6 Sample 11 73.12 37.42 9.92 69.3 63.0
Sample 12 73.79 37.45 9.93 83.8 76.1
Average 73.88 37.44 - - - -
Standard
Deviation 0.28 0.03 - - - -
127
Figure 4.3 Axial stress against axial strain of tri-axial brick property test
Figure 4.4 Shear stress against axial stress of tri-axial property test
Table 4.3 Results of various Mohr-Coulomb strength envelopes
0
10
20
30
40
50
60
70
80
0 0.005 0.01 0.015 0.02
σ1
(M
Pa
)
ε1
Test 1 - 1MPa
Test 2 - 1MPa
Test 3 - 1MPa
Test 4 - 3MPa
Test 5 - 3MPa
Test 6 - 3MPa
Test 7 - 5MPa
Test 8 - 5MPa
Test 9 - 5MPa
Test 10 - 10MPa
Test 11 - 10MPa
Test 12 - 10MPa
0
10
20
30
40
0 20 40 60 80
Sh
ear
stre
ss (
MP
a)
Axial stress (MPa)
1Mpa
3Mpa
5Mpa
10Mpa
strength envelope
Strength
Envelope 1
Strength
Envelope 2
Strength
Envelope 3
Friction angle 44° (Max.) 41° (Min.) 43° (Medium)
Cohesion (MPa) 4.8 9.5 4.3
1 MPa
3 MPa
5 MPa
10 MPa
Strength envelope
128
4.2.3 Mortar
The 20 mortar samples for each mix proportion of cement to lime to sand
(1:2:9/1:1:6) were prepared with the help of the mortar moulds (i.e. PVC pipe
sections, as shown in Figure 4.5 (a)). The required dimension was the same as the
brick cylinder sample for UCS test (Ø 37 × 74 mm). When the mortar was put into
the mortar moulds, a vibrating table was used to get the bubbles out of the moulds.
When the mortar samples were demoulded after 14 days, they were still low in
strength.
Figure 4.5 (a) PVC pipe sections for mortar sample preparation; (b) Mortar
cylinder samples
1) Uni-axial compressive strength test
After 28 days, uni-axial compressive strength tests of mortars in different mix
proportions were carried out using a UCS machine. The loading rate was 0.2
mm/min. The results are shown in Table 4.4. A stronger mortar mix proportion of
1:1:6 seems to be stiffer with a higher Young’s modulus. The load versus
displacement curve obtained from the test data can be seen in Appendix A.
129
Table 4.4 Average UCS test list of different mortar samples
4.2.4 Surrounding soil
1) Shear box tests
Shear box tests (direct shear tests, see Figure 4.6) were utilised to investigate the
properties of soil, such as the friction angle.
The shear box could be split horizontally into two halves. A specimen of Portaway
sand (60 × 60 mm by 30 mm thick, see Figure 4.7 & Figure 4.8) placed in the box
was sheared horizontally by moving the bottom half of the box relative to the top
half at a constant rate of 1 mm/min.
A vertical normal stress was applied during shearing and both the vertical
displacement of the top of the specimen and the horizontal shear displacement were
measured by dial gauges. Failure was prescribed on the plane separating the two
halves of the box. The horizontal shear load was applied to the sand in the box with
the normal force of 0.5, 1 and 1.5 kN. For each dead weight, the shear test was
repeated 3 times; thus, 9 tests were done in total.
Mortar
samples
Mortar Mix
Proportion
Average
Length
Average
Diameter
Failure
Load
Ultimate
Compressive
Strength
Young’s
Modulus
(mm) (mm) (kN) (MPa) (MPa)
Batch 01 1:2:9 73.93 37.57 3.3 3.1 254
Batch 02 1:1:6 73.97 37.62 4.8 4.4 328
130
The shear force versus horizontal displacement curve at different normal stresses is
shown in Figure 4.9. The shear stress versus the normal stress curve is also displayed
in Figure 4.10, whilst Figure 4.11 illustrates the average shear stress versus the
normal stress curve. The results of the shear box test help to obtain the essential soil
properties of the friction angle, as shown in Table 4.5.
Figure 4.6 General view of shear box apparatus
Figure 4.7 Detailed view of shear box sample holder
131
Figure 4.8 Cross section of shear box
Figure 4.9 Shear force against horizontal displacement in shear box test
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 2 4 6 8
Sh
ear
forc
e (k
N)
Horizontal displacement (mm)
0.5kN Test 1
0.5kN Test 2
0.5kN Test 3
1.0kN Test 1
1.0kN Test 2
1.0kN Test 3
1.5kN Test 1
1.5kN Test 2
1.5kN Test 3
Average density: 1832 kg/m3
132
Figure 4.10 Shear stress against normal stress in shear box test
Figure 4.11 Average shear stress against normal stress in shear box test
Table 4.5 Portaway sand partial properties
2) Maximum and minimum density test
Since the density of the soil in the physical model may vary during the compaction,
the maximum and minimum densities of the soil were tested individually, according
0
50
100
150
200
250
300
350
400
450
0 200 400 600
Sh
ear
stre
ss (
kP
a)
Normal stress (kPa)
0.5kN Max.
1.0kN Max.
1.5kN Max.
y = 0.9657x
R² = 0.9858
0
50
100
150
200
250
300
350
400
450
0 200 400 600
Sh
ear
stre
ss (
kP
a)
Normal stress (kPa)
Average shear stress
Linear (Average shear stress)
Soil type Average density Cohesion Friction angle
Portaway sand 1832 kg/m3 0 44˚
133
to BS 1377 - 4: 1990. The density of the soil would also affect the value of the
friction angle in a numerical simulation. The results are shown below:
ρmin.= 1621 kg/m3
ρmax.= 1867 kg/m3
4.2.5 Brickwork (Triplet / Couplet)
1) Introduction
The format of the brickwork specimen comprised a three half-scale brick triplet
sandwich for the UCS test and the shear strength test, with a two half-scale brick
couplet for the tensile strength test. The specimens were prepared separately with
two mortar mix proportions of cement to lime to sand (1:2:9/1:1:6) and tested at 28
days for quality control purposes. The thickness of the mortar was kept at a constant
5 mm, the same as that in physical models.
2) UCS test
Figure 4.12 The uni-axial compressive strength test of the brickwork
134
The uni-axial compressive strength tests were carried out using a Universal Testing
Machine (UTM) from the Zwick/Roell company, in accordance with BS EN 1052 - 1:
1999 (Determination of compressive strength). The capacity of the UTM is 200 kN.
For each mortar mix proportion, 3 triplet specimens were tested at a loading speed of
0.02 mm/s until failure occurred. As can be seen from Figure 4.12, two LVDTs
(Linear Variable Differential Transformer) with a stroke of 10 mm were fixed on
two symmetrical faces for each specimen to measure vertical deformations under the
applied load.
Calculations
Strength
..…………….………..….…N/mm2……………………………….(4.1)
Fi,max (N) is the maximum load reached on an individual brickwork specimen, fi
(N/mm2) is the compressive strength of an individual brickwork specimen, and Ai
(mm2) is the loaded cross-section of an individual brickwork specimen. Thus, the
mean compressive strength of the brickwork is obtained.
Modulus of elasticity
………….………..….…N/mm2……………………………….(4.2)
The modulus of elasticity of an individual brickwork specimen is calculated from the
mean of all measuring positions occurring at a stress equal to one third of the
maximum stress and is the mean strain in an individual brickwork specimen at one
third of the maximum stress achieved.
Ai3
maxFi,=Ei
i
Ai
maxFi,=fi
135
The main results of the uni-axial compressive strength tests of the brickwork are
shown in Table 4.6 and in Appendix A for figures of load versus displacement.
Table 4.6 UCS test list of various brickwork triplets
3) Tensile strength test
The bond between brick and mortar is often considered to be the weakest link in
brickwork. Thus, the brick-mortar interface is one of the most essential features
related to brickwork behaviour.
There are two different failure phenomena occurring in the brick-mortar interface, in
the form of tensile failure and shear failure (Lourenco, 1996).
Therefore, a tensile (bond) strength test was carried out associated with tensile
failure according to the tensile test by Van Der Pluijm (1992), as seen in Figure 4.13;
a shear (bond) strength test was conducted associated with shear failure (see next
section for details).
Mortar Mix
Proportion
Average
Length
Average
Height
Average
Width
Failure
Load
Compressive
Strength
Young’s
Modulus
(mm) (mm) (mm) (kN) (MPa) (GPa)
1:2:9 99.17 105.67 49.17 33.28 6.83 0.219
1:1:6 104 107.667 48.33 39.30 7.83 0.384
136
Figure 4.13 Test specimen of tensile strength after Van Der Pluijm (1992)
Calculations
Strength
……………………………..….N/mm2……………………….…………(4.3)
Fu (N) is the ultimate force reached on an individual brickwork specimen, ft (N/mm2)
is the tensile bond strength of an individual brickwork specimen and A (mm2) is the
cross-section area of an individual brickwork specimen where the crack has occurred.
(Van Der Pluijm, 1997)
Testing of the couplet
The tensile strength test rig was designed and made in the work shop which enables
two bricks to be fixed firmly (see Figure 4.14 (a). The tensile strength tests were
carried out using a ‘Dual olumn Tabletop Universal Testing Machine’ (UTM ) for
mid-range testing from the Instron Company (see Figure 4.15). The capacity of this
UTM is 50 kN.
A
Fu=ft
137
Figure 4.14 (a) The tensile strength test before loading; (b) The tensile strength
test after loading
Figure 4.15 The Tabletop Universal Testing Machine after Instron Ltd.
As can be seen from Figure 4.14 (b), after each test the brickwork couplet was
separated in the brick / mortar bond area on one or two brick faces (see Figure 4.16).
i.e. tensile failure occurred at the brick / mortar interface. It shows a good agreement
138
with Lenczner (1972), who found that the tensile strength of brickwork was
governed by the tensile bond strength.
Figure 4.16 Tensile failures at brick / mortar interface
Table 4.7 lists the results of average tensile strength tests which helped to draw
Figure 4.17 and shows the tensile strength difference between two mortar mix
proportions. Generally speaking, as the strength of mortar mix proportion increased,
the tensile strength of brickwork also increased correspondingly. More details of the
results are shown in Appendix A.
Table 4.7 The tensile strength test results of brickwork triplets
Brickwork
Triplets
Mortar Mix
Proportion
Average
Length
Average
Width
Tensile
Failure Load
Tensile
Strength
(mm) (mm) (N) (MPa)
Batch 01 1:2:9 103.8 45.8 467.09 0.09681
Batch 02 1:1:6 100.367 50.3667 1230.05 0.24369
139
Figure 4.17 Tensile strength of two mortar mix proportions
4) Shear strength test
Figure 4.18 Test rig for shear strength test
The shear strength test was carried out in accordance with the provision of BS EN
1052 - 3: 2002 (Determination of initial shear strength).
A test rig (in Figure 4.18) was especially designed and fabricated for the testing of
the half-scale brick triplet specimens. A spring was used to exert and adjust the
different applied precompressive forces.
0
0.1
0.2
0.3
0 1 2 3
Av
era
ge
Ten
sile
Str
eng
th
(MP
a)
Mortar Mix Proportion Type
Mortar Mix
Proportion
1:2:9
Mortar Mix
Proportion
1:1:6
140
The vertical load was also applied by the same UTM from the Instron Company as
used for the tensile strength test.
For this test, the vertical load was at a loading speed of 1 mm/min until shear failure
occurred. Vertical displacement was caught automatically by the LVDTs built inside
the loading machine.
According to the standard, two steel plates of 6 mm thickness with two steel bars of
6 mm diameter were placed underneath the specimen in a certain position.
Meanwhile, two steel bars of 6 mm in diameter were placed between two steel plates
of 6 mm thickness above the specimen on which the load was applied (see Figure
4.19).
For each mortar mix proportion, three triplet specimens were tested at each of 3
precompression loads horizontally, which gave precompressive stresses of
approximately 0.002 N/mm2, 0.006 N/mm
2 and 0.01 N/mm
2.
Calculations
Strength
….……………………………N/mm2………………….………...(4.4)
……………………..…………..N/mm2….…….………….……….(4.5)
Fi,max (N) is the maximum shear load reached on an individual brickwork specimen,
Fpi (N) is the precompressive force, fshi (N/mm2) and fpi (N/mm
2) are the shear
strength and precompressive stress of an individual brickwork specimen respectively,
while Ai (mm2) is the cross-section area of an individual brickwork specimen parallel
2Ai
maxFi,=fshi
Ai
Fpi=fpi
141
to the bed joints. The mean initial shear strength is recorded at zero precompressive
stress from the intercept of the fshi against fpi line with the vertical axis. The angle
of internal friction and cohesion could also be obtained.
Figure 4.19 Dimensions for shear strength tests (Mohammed, 2006)
Figure 4.20 Shear failures in the brick / mortar bond area
All the shear failures were in the brick / mortar bond area, either on one or divided
between two brick faces, as Figure 4.20 shows.
L (mm) e (mm) d (mm) t (mm)
Mean dimensions 104 6.5 6 6
142
The main results of the shear strength test are shown in Table 4.8, Figure 4.21,
Figure 4.22 and the figures in Appendix A. The ultimate shear strength of brickwork
does not increase dramatically as the mortar strength is increased. It proves that the
shear bond was normally independent of mortar strength (Lenczner, 1972).
Table 4.8 The shear strength test results of brickwork triplets
Figure 4.21 Average shear stress against precompression stress of brickwork
triplet (1:2:9)
y = 1.31x + 0.04
R² = 0.99
0.039
0.041
0.043
0.045
0.047
0.049
0.051
0.053
0 0.005 0.01 0.015
Sh
ear
stre
ss (
MP
a)
Precompression stress (MPa)
Average shear stress
Linear (Average
shear stress)
Brickwork
Triplets
Mortar
Mix
Proportion
Average Length
(mm)
Average Width
(mm)
Cohesion
(MPa)
Friction Angle
Batch 01 1:2:9 98.55 50.13 0.0389 52°
Batch 02 1:1:6 99.02 50.43 0.1845 55°
143
Figure 4.22 Average shear stress against precompression stress of brickwork
triplet (1:1:6)
4.3 Modelling issues of brick-lined tunnels
4.3.1 Modelling approaches
Both simplified micro-modelling and macro-modelling strategies are employed in
this research and compared with each other.
The finite difference method (FDM) is used in FLAC programme to build numerical
models corresponding to a macro-modelling strategy, while a simplified micro-
modelling strategy is applied to the UDEC programme (Distinct element method).
(see Chapter 2 literature review for more details)
y = 1.44x + 0.18
R² = 0.89
0.1860
0.1880
0.1900
0.1920
0.1940
0.1960
0.1980
0.2000
0.2020
0 0.005 0.01 0.015
Sh
ear
stre
ss (
MP
a)
Precompression stress (MPa)
Average shear stress
Linear (Average shear
stress)
144
4.4 Introduction to FLAC
4.4.1 General introduction
In this research, the finite difference method (FDM) is mainly used to build
numerical models corresponding to the macro-modelling strategy. It is one of the
oldest numerical techniques for the solution of differential equations.
FLAC (Fast Lagrangian Analysis of Continua) is a two-dimensional commercial
program developed by the Itasca Consulting Group Inc., using the explicit finite
difference method. The program was originally developed for mining and
geotechnical engineering applications, such as underground construction. It could
simulate the nonlinear behaviour of structures built of soil, rock or other materials
undergoing plastic collapse and flow when their yield limits in shear or tension are
reached.
FLAC is also capable of solving a wide range of complex problems in mechanics
with the help of several built-in constitutive models. In FLAC Version 6.0, there are
12 basic constitutive models divided into null, elastic and plastic model groups.
In FLAC, a powerful built-in programming language called FISH enables the user to
define new variables, write new functions to extend the application of FLAC or
implement one’s own constitutive models. FISH was developed to assist users who
would like to conduct work that is difficult or unavailable with existing codes.
The main characteristics and implementation of FLAC are presented with reference
to the manual of FLAC (Itasca, 2008).
145
In FLAC, it is not necessary to form a global stiffness matrix. Coordinates at each
time step are updated in large-strain mode. As the incremental displacements are
added to the coordinates, the grid moves and deforms with the corresponding
material. This is termed a ‘Lagrangian’ formulation. It is different from a
formulation called ‘Eulerian’, in which the material moves and deforms relative to a
fixed grid.
4.4.2 Fields of application
FLAC has been used primarily for analysis and design in the fields of mining,
underground construction and so on. The analysis of progressive failure and collapse
is achievable by its explicit, time-marching solution of the full equations of motion.
Some example applications of FLAC are listed below:
a) Evaluation of the influence of fault structures in mine design;
b) Simulation of various rock reinforcement systems, such as rockbolts, steel beams
and tunnel liners, as well as soil reinforcement systems such as tiebacks and soil
nailing, using structural elements;
c) Studies in salt and potash mine design by establishing the creep model;
d) Research into the process and mechanisms of localisation and the evolution of
shear bands in frictional materials;
e) Studies of the performance of deep underground repositories for high-level
radioactive waste by setting up the thermal model;
f) Potential applications, including analyses of earth-retaining structures and
earthen slopes under drained and undrained loading in addition to calculations of
bearing capacity and the settlement of foundations;
146
g) Analyses in earthquake engineering, such as dam stability, soil structure
interaction and liquefaction; studies of the effects of explosive loading, such as
underground blasting;
h) In this research, FLAC was used to develop a two-dimensional plane-strain
model as its basic formulation.
4.4.3 Comparison with the Finite Element Method
1) Similarities and differences
Over the years, the finite difference method (FDM) has always been compared with
the finite element method (FEM) as applied to computer programs for numerical
simulation.
Both methods produce a range of algebraic equations to solve. Although these
algebraic equations are derived differently in FDM and FEM, the resulting equations
are the same.
At the same time, there are some distinctions between these two methods. It should,
however, be stressed that these different features are mainly due to established habits.
For instance, in finite difference programs, finite difference equations are
regenerated at each step for efficiency, while finite element programs usually
combine element matrices into a global stiffness matrix. An explicit, time-marching
scheme is commonly used in finite difference programs to solve the algebraic
equations, while finite element programs often use implicit, matrix-oriented
solutions. Table 4.9 compares the explicit and implicit methods.
147
Table 4.9 Comparison of explicit and implicit solution methods (Itasca, 2008)
2) Advantages and disadvantages
There are several outstanding advantages of FLAC using explicit methods: most
importantly, the iteration process is not necessary when computing stresses from
strains in an element, whether the constitutive law is linear or nonlinear.
FLAC using explicit methods is better for modelling ill-behaved systems (e.g.,
nonlinear, large-strain, physical instability); they are not efficient enough for linear,
small-strain issues.
Explicit Implicit
Timestep must be smaller than a critical
value for stability.
Timestep can be arbitrarily large, with
unconditionally stable schemes.
Small amount of computational effort per
timestep.
Large amount of computational effort
per timestep.
No significant numerical damping
introduced for dynamic solution.
Numerical damping dependent on
timestep present with unconditionally
stable schemes.
No iterations necessary to follow nonlinear
constitutive law.
Iterative procedure necessary to follow
nonlinear constitutive law.
Provided that the timestep criterion is
always satisfied, nonlinear laws are always
followed in a valid physical way.
Always necessary to demonstrate that
the abovementioned procedure is: (a)
stable; and (b) follows the physically
correct path (for path-sensitive
problems).
Matrices are never formed. Memory
requirements are always at a minimum.
No bandwidth limitations.
Stiffness matrices must be stored. Ways
must be found to overcome associated
problems such as bandwidth. Memory
requirements tend to be large.
Since matrices are never formed, large
displacements and strains are
accommodated without additional
computing effort.
Additional computing effort needed to
follow large displacements and strains.
148
FLAC could handle any constitutive model without adjustment to the solution
algorithm, whereas many finite element codes need different solution algorithms for
different constitutive models.
FLAC elements are in a row-and-column fashion rather than in a sequential fashion,
which makes it easier to identify elements.
One significant disadvantage is that FLAC takes a longer time to simulate linear
problems than equivalent finite element programs.
4.4.4 General solution procedure
To start with, three fundamental components of a problem must be specified in order
to establish and run a numerical model with FLAC.
a) A finite difference grid;
b) Constitutive behaviour and material properties; and
c) Boundary and initial conditions.
After these conditions are defined in a numerical model, the initial equilibrium state
is calculated for the model. An alteration is then performed such as excavation or
changing boundary conditions; the resulting response of the model is calculated. The
general solution procedure, illustrated in Figure 4.23, represents the sequence of
processes that occurs in the physical environment.
149
Figure 4.23 General solution procedure (Itasca, 2008)
Model makes sense
Results unsatisfactory
No
Yes
More
tests
needed
Acceptable result
Examine
the model response
Start
MODEL SETUP
1. Generate grid, deform to desired shape
2. Define constitutive behaviour and material properties
3. Specify boundary and initial conditions
Step to equilibrium state
PERFORM ALTERATIONS
For example,
Excavate material
Change boundary conditions
1. Specify boundary and initial
Step to solution
Examine
the model response
Parameter study
needed
End
150
4.4.5 Further developments
Itasca Consulting Group Inc. has also developed the FLAC3D
program based on the
well-established FLAC program. Thus, it extends the analysis capability of FLAC
into three dimensions, mainly simulating the behaviour of certain three-dimensional
geotechnical structures, which FLAC could hardly simulate.
4.5 Numerical modelling of physical models using FLAC
4.5.1 Materials and interface properties
The Mohr-Coulomb constitutive model is used during the numerical modelling of
FLAC. Most of the properties needed are derived from laboratory property tests, as
mentioned in Section 4.2 Programme of material testing.
Interfaces (Joints) are used to represent planes on which sliding or separation would
occur. In particular, the interface has some essential stiffness factors such as normal
and shear stiffness (JKn and JKs) between two blocks, which may contact each other.
Other important strength factors are cohesion, friction angle and tensile bond
strength, etc.
The interface properties are classified into three categories as follows (Itasca, 2008):
a) Glued
Where there is no slip or separation allowed in the interface. Only joint normal and
shear stiffness are required.
151
b) Unglued
o Unbonded: Where the slip is allowed without any tensile bond. Factors of
JKn, JKs, cohesion, dilation angle and friction angle are needed.
o Bonded: Where there is no slip or separation allowed unless the
strength(s) is exceeded. Factors for the ‘unbonded’ category and also
tensile bond strength are required.
Since a macro-modelling strategy is used in FLAC, only the interfaces between
brickwork and the soil belong to ‘unbonded’ category. Stiffness and strength
properties (JKn, JKs, cohesion, dilation and friction angle) are required.
For interfaces used to glue two blocks, i.e. preventing any slip or separation, a good
rule-of-thumb for the value of JKn and JKs is to set to ten times the equivalent
stiffness of the stiffest neighbouring zone (Itasca, 2008).
Figure 4.24 Zone dimension used in stiffness calculation
…………………………………………………. (4.6)
……………………………………………………………………….. (4.7)
……………………………………………………………………….. (4.8)
)min
3
4
(max 10JKsJKnz
GK
v
EK
213
v
EG
12
Interface
∆z min
152
Where K and G are the bulk and shear moduli respectively, ∆zmin is the smallest
width of an adjoining zone in the normal direction; E is the Young’s modulus, while
v is the Poisson’s ratio. (see Figure 4.24)
In other unglued circumstances, unbonded and bonded, the value of both JKn and
JKs could be reduced according to the equivalent stiffness of the neighbouring zone.
In the following sections, the joint stiffness properties have been calculated
according to Equations (4.6) to (4.8), and joint strength properties have been
estimated from laboratory property tests in Section 4.2 Programme of material
testing.
4.5.2 Model generation
The tunnel was subjected to the self weight of the homogeneous surrounding soil.
Grid generation, with very fine meshes as well as proper aspect ratio (ratio of height
to width of a zone), was made to fit the physical shape of the model and to pursue
more results that are accurate.
The next step was to create and assign materials and their properties to the zones
within the grid. Here brickwork properties were assigned in blue while surrounding
soil properties were in green, as is shown in Figure 4.25, with both prescribed
according to the Mohr-Coulomb model.
Thereafter, boundary conditions for the physical model were assigned so that roller
boundary conditions were applied to two sides and along the bottom of the model.
Moreover, pinned boundary conditions were also applied to the bottom corners of
the tunnel, shown in Figure 4.25. Gravity of 9.81 m/s2 was set. The model was then
153
set to equilibrium state, simulating the preparation procedure of the physical model
just before loading.
Vertical loading was then added at certain interval until the tunnel failed, in order to
simulate the physical model test. That required a change in the boundary conditions
as displacement-control loading and a step to the solution. Afterwards, the model
response was analysed.
Figure 4.25 FLAC model grids with boundary conditions
4.5.3 Parametric study
In FLAC, a macro-modelling strategy (see Section 2.5.1 for details) is used, which is
to consider the brick, mortar and brick / mortar interface smeared out in a
homogeneous anisotropic continuum.
154
Thus, the mechanical properties of brickwork below were selected for the purpose of
parametric study: Poisson’s ratio (v), Young’s modulus (E), cohesion (c), friction
angle (φ) and density (ρ).
In addition, the interface properties of brickwork / soil were estimated for use after
the parametric study of joint stiffness and joint friction angle.
The effects of these properties on the stress and deformation conditions have been
studied with both uniform and concentrated loading until failure.
The properties of surrounding soil were always kept the same during the whole
process of numerical simulation, based on the laboratory tests (see Table 4.10).
Table 4.10 Surrounding soil (Portaway sand) properties
*:Young’s modulus and Poisson’s ratio were referring to Juspi, 200 ; Tr is the
tensile strength.
1) Uniform load
Baseline numerical model (1:1:6)
Table 4.11 lists the mechanical properties assigned to brickwork with mortar mix
proportion of 1:1:6 and interface properties of brickwork and soil as a baseline from
the laboratory work, Equations (4.6) to (4.8) and some estimation, such as joint
friction and joint cohesion. Further adjustment of some estimated properties would
be made after the parametric study.
Surrounding soil
ρ (kg/m³) E (MPa) v c (MPa) φ Tr (MPa)
1832 26* 0.3* 0 44° 0*
155
Table 4.11 Brickwork (mix proportion 1:1:6) and brickwork / soil joint
properties
*: Poisson’s ratio of the brickwork and the friction angle of the joint (Jφ) were
initially referring to Idris et al., 2008.
Figure 4.26 and Figure 4.27 illustrate the displacement vectors and plastic state of
the baseline numerical model individually, with the image in the lower left-hand
corner showing the physical model test result. Both of the figures are coincident with
the physical model test, with a similar deformation trend and shear failure at the
tunnel sides.
The tunnel crown displacement curve of the FLAC baseline numerical model is
compared with that of the physical model test 1 in Figure 4.28, which seems to be
much stiffer than the physical model result.
Thus, further parametric studies of the mechanical properties are needed to approach
the proper simulation of the physical model test 1 in the next part.
Brickwork (1:1:6)
ρ (kg/m³) E (MPa) v c (MPa) φ Tr (MPa)
1732 384.33 0.2* 0.1845 55° 0.2437
Brickwork / soil joint
JKn (GPa/m) JKs (GPa/m) Jc (MPa) Jφ JTr (MPa)
112.97 112.97 0 25* 0
156
Figure 4.26 Displacement vectors of numerical model (1:1:6) during uniform
static load compared with the physical model
Figure 4.27 Plastic state of numerical model (1:1:6) compared with the physical
model
157
Figure 4.28 Physical model 1 vs. FLAC baseline A curves
Parametric study
FLAC model A1: After increasing the Poisson’s ratio of the brickwork to 0.3, there
was no significant effect on stiffness (see Figure 4.29). Thus, the Poisson’s ratio of
0.2 would be used through the parametric study of the numerical model (1:1:6).
Figure 4.29 Physical model 1 vs. FLAC baseline A & model A1 curves
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC Baseline A
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC Baseline A
FLAC A1
158
FLAC models A2 and A3: The maximum and minimum values of Young’s
modulus (E) obtained from the UCS test of brickwork (1:1:6) were then input in
FLAC models A2 and A3, which more or less varied the stiffness (see Figure 4.30).
Figure 4.30 Physical model 1 vs. FLAC baseline A & model A2 - A3 curves
FLAC models A4 and A5: The strength of the baseline model seemed to be much
stronger than that of the physical model. In order to match the ultimate pressure of
the physical model, the friction angle of the brickwork was reduced to 50° and 52° in
FLAC models A4 and A5 respectively. FLAC model A4 performed very well and
approached the ultimate value and crown displacement as physical model test 1,
while FLAC model A5 showed a larger ultimate value in Figure 4.31. Therefore, in
the following parametric study, the result of FLAC model A4 would be compared as
a new baseline.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC Baseline A
FLAC A2
FLAC A3
159
Figure 4.31 Physical model 1 vs. FLAC baseline A & model A4 - A5 curves
FLAC models A6, A7 and A8: Next, the cohesion of the brickwork was varied from
0.14 to 0.2 MPa, up to 24.1% difference from FLAC model A4. The increase in the
cohesion also increased the ultimate pressure and the stiffness. As can be seen in
Figure 4.32, FLAC model A7 seemed to be closer to the physical model test, where
the stiffness was even lower than FLAC model A4. In this case, the new baseline
FLAC model A4 was replaced by FLAC model A7.
Figure 4.32 Physical model 1 vs. FLAC model A4 & model A6 - A8 curves
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC Baseline A
FLAC A4
FLAC A5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC A4
FLAC A6
FLAC A7
FLAC A8
160
FLAC models A9, A10 and A11: Since the friction angle of brickwork / soil
interface was estimated with reference to Idris et al., 2008, the parametric study of
the friction angle was carried out by increasing the value from 30°, to 35° and then
40°. The stiffness in these models was similar. However, as the friction angle
increased, the ultimate pressure also increased. The curve does not match the
physical model result and is toward the opposite direction (see Figure 4.33). FLAC
model A7 was better than other models in simulating the physical model.
Figure 4.33 Physical model 1 vs. FLAC model A7 & model A9 - A11 curves
FLAC models A12 and A13: Again, the maximum and minimum value of Young’s
modulus (E) was employed in FLAC models A12 and A13. This time the increased
Young’s modulus also led to an increase in stiffness and ultimate pressure, while the
minimum value resulted in similar stiffness and lower ultimate value (see Figure
4.34). FLAC model A7 was an appropriate model compared with physical model 1.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40 50 60 70
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC A7
FLAC A9
FLAC A10
FLAC A11
161
Figure 4.34 Physical model 1 vs. FLAC model A7 & model A12 - A13 curves
FLAC model A14: At last, the joint stiffness was reduced according to Equations
(4.6) to (4.8). As can be seen from Figure 4.35, the result of FLAC model A14 seems
to be removed from that of physical model test 1.
Ultimately, FLAC model A7 was proved to be the most appropriate one to simulate
the physical model test 1 (see Figure 4.36).
In addition, the pressure-displacement curve at one quarter across the tunnel arch
obtained by photogrammetry (Figure 3.38 shown in Chapter 3) was compared with
the proper FLAC model, as seen in Figure 4.37, from 0 kN to 590 kN load. The
curve by photogrammetry shows a slightly higher stiffness, although the
displacement difference is within 2.5 mm at the same pressure of 0.89 MPa.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC A7
FLAC A12
FLAC A13
162
Figure 4.35 Physical model 1 vs. FLAC model A7 & A14 curves
Figure 4.36 Physical model 1 vs. FLAC model A curves
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC A7
FLAC A14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC A
163
Figure 4.37 Photogrammetry at 1/4 vs. FLAC model A curves
Table 4.12, Table 4.13 and Table 4.14 have clearly displayed the progress of the
parametric study.
Table 4.12 Brickwork parametric study of Poisson’s ratio, Young’s modulus
and friction angle (Mix proportion of 1:1:6)
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Pre
ssu
re (
MP
a)
One quarter disp (mm)
Photogrammetry
FLAC
E (MPa) v c (MPa) φ JKn = JKs (GPa/m) Jφ
Baseline A 384.33 0.2 0.1845 55° 112.97 25°
FLAC A1 384.33 0.3 0.1845 55° 136.87 25°
FLAC A2 553 0.2 0.1845 55° 162.55 25°
FLAC A3 249 0.2 0.1845 55° 73.19 25°
FLAC A4 384.33 0.2 0.1845 50° 112.97 25°
FLAC A5 384.33 0.2 0.1845 52° 112.97 25°
Photogrammetry
FLAC A
164
Table 4.13 Parametric study of the brickwork cohesion (1:1:6)
Table 4.14 Parametric study of brickwork Young’s modulus, joint friction angle
and stiffness (1:1:6)
E (MPa) v c (MPa) φ JKn = JKs (GPa/m) Jφ
FLAC A4 384.33 0.2 0.1845 50° 112.97 25°
FLAC A6 384.33 0.2 0.2 (8%) 50° 112.97 25°
FLAC A7 384.33 0.2 0.16 (13.3%) 50° 112.97 25°
FLAC A8 384.33 0.2 0.14 (24.1%) 50° 112.97 25°
E (MPa) v c (MPa) φ JKn = JKs (GPa/m) Jφ
FLAC A7 384.33 0.2 0.16 50° 112.97 25°
FLAC A9 384.33 0.2 0.16 50° 112.97 30°
FLAC A10 384.33 0.2 0.16 50° 112.97 35°
FLAC A11 384.33 0.2 0.16 50° 112.97 40°
FLAC A12 553 0.2 0.16 50° 162.55 25°
FLAC A13 249 0.2 0.16 50° 73.19 25°
FLAC A14 384.33 0.2 0.16 50° 56.49 25°
165
Baseline numerical model (1:2:9)
As in the numerical modelling of brickwork (1:1:6), the baseline numerical model B
was first developed with the properties listed in Table 4.15. Compared with physical
model test 2, the FLAC baseline model B is less stiff. Thus, more parametric studies
are required to obtain a better simulation of physical model test 2.
Table 4.15 Brickwork (mix proportion of 1:2:9) and brickwork / soil joint
properties
*: Poisson’s ratio of the brickwork and the friction angle of the joint (Jφ) were
initially referring to Idris et al., 2008.
Figure 4.38 Physical model 2 vs. FLAC baseline B curves
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC Baseline'
Brickwork (1:2:9)
ρ (kg/m³) E (MPa) v c (MPa) φ Tr (MPa)
1672.5 218.67 0.2* 0.0389 52° 0.0968
Brickwork / soil joint
JKn (GPa/m) JKs (GPa/m) Jc (MPa) Jφ JTr (MPa)
64.28 64.28 0 25* 0
Physical model test 2
FLAC Baseline B
166
Parametric study
FLAC models B1 and B2: The maximum and minimum values of Young’s modulus
(E) obtained from the UCS test of brickwork (1:2:9) were used to model FLAC B1
and B2. As can been seen in Figure 4.39, the change in Young’s modulus has not
significantly affected the curve to approach the experiment curve. In this case, the
variation in strength properties is studied in the following part.
Figure 4.39 Physical model 2 vs. FLAC baseline B & model B1 - B2 curves
FLAC model B3 and B4: The reduction of the friction angle of the brickwork to 50°
in FLAC B3 also reduced the stiffness. However, as the friction angle increased to 55°
in FLAC B4, there was still a large difference compared to physical model test 2 (see
Figure 4.40). It was then necessary to check the cohesion influence.
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC Baseline'
FLAC 1'
FLAC 2'
Physical model test 2
FLAC Baseline B
FLAC B1
FLAC B2
167
Figure 4.40 Physical model 2 vs. FLAC baseline B & model B3 - B4 curves
FLAC models B5, B6, B7 and B8: The cohesion of the brickwork was increased
step by step, from 0.05 MPa to 0.1 MPa (increased by 28.53% to 157.07%, see Table
4.17). Thus the stiffness and the ultimate pressure were increased and to become
closer to the experiment result (see Figure 4.41). In these models, FLAC B6 with the
increased cohesion of 0.07 MPa (increased by 79.94%) seemed to be better than the
FLAC baseline model B. The cohesion value input was not as large as 0.09 MPa or
even 0.1 MPa, which increased by more than 100% of the laboratory value. The
FLAC baseline B was then replaced by FLAC model B6 as a new baseline.
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC Baseline'
FLAC 3'
FLAC 4'
Physical model test 2
FLAC Baseline B
FLAC B3
FLAC B4
168
Figure 4.41 Physical model 2 vs. FLAC baseline B & model B5 - B8 curves
FLAC models B9 and B10: Next, the maximum and minimum values of Young’s
modulus (E) were input in FLAC models B9 and B10. Figure 4.42 illustrates that the
variation of Young’s modulus did not make a big difference in terms of stiffness and
ultimate load.
Figure 4.42 Physical model 2 vs. FLAC model B6 & model B9 - B10 curves
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC Baseline'
FLAC 5'
FLAC 6'
FLAC 7'
FLAC 8'
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC 6'
FLAC 9'
FLAC 10'
Physical model test 2
FLAC Baseline B
FLAC B5
FLAC B6
FLAC B7
FLAC B8
Physical model test 2
FLAC B6
FLAC B9
FLAC B10
169
FLAC model B11: Finally, the joint stiffness was reduced by 50% in FLAC B11
according to Equations 4.1 to 4.3, which differed from the experiment result (see
Figure 4.43).
Figure 4.43 Physical model 2 vs. FLAC model B6 & model B11 curves
After the parametric study, FLAC B6 was proved to be the most suitable model to
simulate physical model test 2, as shown in Figure 4.44.
Figure 4.44 Physical model 2 vs. FLAC model B curves
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC 6'
FLAC 11'
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC'
Physical model test 2
FLAC B6
FLAC B11
Physical model test 2
FLAC B
170
Table 4.16, Table 4.17 and Table 4.18 list the progress of the parametric study as
below.
Table 4.16 Brickwork parametric study of Young’s modulus and friction angle
(Mix proportion of 1:2:9)
Table 4.17 Parametric study of the brickwork cohesion (1:2:9)
Table 4.18 Parametric study of brickwork Young’s modulus and joint stiffness
(1:2:9)
E (MPa) v c (MPa) φ JKn = JKs (GPa/m)
Baseline B 218.67 0.2 0.0389 52° 64.28
FLAC B1 233 0.2 0.0389 52° 68.49
FLAC B2 211 0.2 0.0389 52° 62.02
FLAC B3 218.67 0.2 0.0389 50° 64.28
FLAC B4 218.67 0.2 0.0389 55° 64.28
E (MPa) v c (MPa) φ JKn = JKs (GPa/m)
Baseline 218.67 0.2 0.0389 52° 64.28
FLAC B5 218.67 0.2 0.05 (28.53%) 52° 64.28
FLAC B6 218.67 0.2 0.07 (79.94%) 52° 64.28
FLAC B7 218.67 0.2 0.09 (131.36%) 52° 64.28
FLAC B8 218.67 0.2 0.1 (157.07%) 52° 64.28
E (MPa) v c (MPa) φ JKn = JKs (GPa/m)
FLAC B6 218.67 0.2 0.07 52° 64.28
FLAC B9 233 0.2 0.07 52° 68.49
FLAC B10 211 0.2 0.07 52° 62.02
FLAC B11 218.67 0.2 0.07 52° 32.14
171
2) Concentrated load
Baseline numerical model (1:2:9)
The same properties, for baseline model under concentrated load, were used as under
uniform load (see Table 4.15). The loading area was 0.3 m wide. The crown
displacement curve of the FLAC baseline model C is far removed from that of
physical model test 3 (see Figure 4.45).
Figure 4.45 Physical model 3 vs. FLAC baseline C curves
Parametric study
FLAC models C1, C2, C3 and C4: From the experience obtained, the cohesion of
the brickwork largely influenced the curve behaviour. Therefore, the cohesion was
varied at first to approach the experiment curve, from 0.07 MPa to 0.2 MPa. As can
be seen from Figure 4.46, an increase in the cohesion also increases the stiffness of
the crown displacement curve. The curve of FLAC C4 with 0.2 MPa cohesion was
closest to that of the physical model.
0
0.2
0.4
0.6
0.8
0 50 100
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
FLAC Baseline''
Physical model test 3
FLAC Baseline C
172
Figure 4.46 Physical model 3 vs. FLAC baseline C & model C1 - C4 curves
Therefore, FLAC C4 was the best model to match the physical model. However, the
cohesion used (0.2 MPa) was more than 5 times larger than the laboratory result
(0.0389 MPa), shown in Figure 4.47. The reason might be that the FLAC software
with macro-modelling was not able to simulate the model under concentrated load
very well.
Figure 4.47 Physical model 3 vs. FLAC model C curves
0
0.2
0.4
0.6
0.8
0 50 100
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
FLAC Baseline''
FLAC 1''
FLAC 2''
FLAC 3''
FLAC 4''
0
0.2
0.4
0.6
0.8
0 5 10 15 20 25
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
FLAC''
Physical model test 3
FLAC Baseline C
FLAC C1
FLAC C2
FLAC C3
FLAC C4
Physical model test 3
FLAC C
173
The progress of the parametric study has been displayed in Table 4.19.
Table 4.19 Parametric study of the brickwork cohesion under concentrated load
4.5.4 Results analysis of the parametric study
As discussed in Section 4.5.3 , parametric studies in the FLAC models for the
simulations of physical model tests under distributed and concentrated load have
been conducted and presented respectively. They focus on both stiffness and strength
properties of the brickwork and the brickwork / soil joint.
1) The effect of stiffness properties
Brickwork stiffness
Taking numerical models (1:1:6) for example, the obtained results have shown that
there is little change on the crown displacement due to the increase in the Poisson’s
ratio; the variation in Young’s modulus of the brickwork affects 3.5% to 13% of the
crown displacement behaviour, which is compared to the crown displacement of the
FLAC baseline A.
E (MPa) v c (MPa) φ JKn = JKs (GPa/m) Jφ
Baseline C 218.67 0.2 0.0389 52° 64.28 25°
FLAC C1 218.67 0.2 0.07 (79.94%) 52° 64.28 25°
FLAC C2 218.67 0.2 0.1 (157.07%) 52° 64.28 25°
FLAC C3 218.67 0.2 0.15 52° 64.28 25°
FLAC C4 218.67 0.2 0.2 52° 64.28 25°
174
Brickwork / soil joint stiffness
The interface stiffness (JKn & JKs) reduction in value to 50% decreases the overall
stiffness to some extent, as shown in Figure 4.35.
2) The effect of strength properties
Brickwork strength
As can be seen from Figure 4.31 and Figure 4.32, the decrease of friction angle
increases the crown displacement up to 75% of that of the FLAC baseline A, at
1.5MPa loading level; also the cohesion changes largely affect the mechanical
behaviour of the brickwork tunnel.
Brickwork / soil joint strength
The increase in joint friction angle slightly changes the crown displacement curve
(see Figure 4.33).
3) Comments
The results of the parametric study indicate that both the friction angle and cohesion
have a remarkable influence on the brick-lined tunnel mechanical behaviour and the
most important parameter is the cohesion. It shows a good agreement with Idris et al.
(2008) on the property study of masonry blocks.
The rest of the factors considered (Poisson’s ratio, Young’s modulus of the
brickwork, joint stiffness and friction angle) do not have a significant influence on
the mechanical behaviour of the brick-lined tunnel.
175
4.5.5 Modelling results
1) Uniform load
Numerical model (1:1:6)
The mechanical behaviour of the chosen FLAC model A (FLAC A7) at certain
loading level (displacement vectors and plastic state) is shown in Figure 4.48 and
Figure 4.49, which reasonably simulated the physical model test 1.
Figure 4.48 Displacement vectors of FLAC model A (1:1:6)
FLAC (Version 6.00)
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Displacement vectors
max vector = 6.810E-02
0 2E -1
Boundary plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Displacement vectors 1:1:6
176
Figure 4.49 Plastic state of FLAC model A (1:1:6)
Numerical model (1:2:9)
Similarly, the mechanical behaviour of the chosen FLAC model B (FLAC B6) at
certain loading level (displacement vectors and plastic state) is shown in Figure 4.50
and Figure 4.51, which reasonably simulated the physical model test 2.
Figure 4.50 Displacement vectors of FLAC model B (1:2:9)
FLAC (Version 6.00)
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state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
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0.200
0.600
1.000
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-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state 1:1:6
FLAC (Version 6.00)
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Displacement vectors
max vector = 6.015E-02
0 2E -1
Boundary plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Displacement vectors (1:2:9)
177
Figure 4.51 Plastic state of FLAC model B (1:2:9)
2) Concentrated load
Additionally, the mechanical behaviour of the FLAC model C (FLAC C4) at certain
loading level (for displacement vectors and plastic state, see Figure 4.52 and Figure
4.53) may not represent the real behaviour, as shown in physical model test 3.
Figure 4.52 Displacement vectors of FLAC model C (1:2:9) under concentrated
load
FLAC (Version 6.00)
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state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
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0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state (1:2:9)
FLAC (Version 6.00)
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Displacement vectors
max vector = 2.149E+02
0 5E 2
Boundary plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Concentrated load_Displacement vectors
178
Figure 4.53 Plastic state of FLAC model C (1:2:9) under concentrated load
4.6 Introduction to UDEC
4.6.1 General introduction
In this research, a simplified micro-modelling strategy is applied to the UDEC
programme.
UDEC (Universal Distinct Element Code) is a two-dimensional numerical program
also developed by Itasca Consulting Group Inc., based on the distinct element
method (DEM) for discontinuum modelling. UDEC could simulate the behaviour of
discontinuous media, such as a jointed rock mass and an assemblage of discrete
masonry blocks subjected to static or dynamic loading. UDEC is based on a
“Lagrangian” calculation scheme, which is well-suited to model the large
movements and rotations of a blocky system.
FLAC (Version 6.00)
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state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
At Yield in Tension
Grid plot
0 5E -1
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0.600
1.000
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-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Concentrated load_Plastic state
179
Deformable blocks could be subdivided into a mesh of finite-difference elements,
with each element responding according to a prescribed linear or nonlinear stress-
strain law. Linear or nonlinear force-displacement relations for movement both in the
normal and shear direction also govern the relative motion of the discontinuities.
Similar to FLAC, UDEC also contains FISH to define new variables and functions.
FISH permits (UDEC Manual, 2005):
a) Custom property variations in the grid (e.g., nonlinear increase of strength with
depth);
b) Plotting and printing of user-prescribed variables;
c) Implementation of special joint generators;
d) Specification of unusual boundary conditions; variations in time and space;
e) Automation of parameter studies.
4.6.2 Fields of application
The nature of a jointed rock mass (i.e., the internal structure and initial stress state) is
unknown and unknowable to a large extent. Thus, it would be impossible to make an
identical model of a rock mass system by UDEC. Nevertheless, an understanding of
the response of a jointed rock mass can be achieved using UDEC. Thus, it could
improve the engineering understanding of the relative impact of various phenomena
on rock mechanics design. In this way, the engineer could investigate and predict
potential failure mechanisms associated with a jointed rock mass.
The analysis was conducted primarily in the field of rock engineering, ranging from
studies of the progressive failure of rock slopes to evaluations of the influence of
rock joints, faults, bedding planes, etc. on underground excavations and rock
180
foundations. Various rock reinforcement systems, such as grouted rockbolting and
shotcrete, have been simulated using a structural element set in the program.
UDEC has been applied mostly in studies related to mining engineering, such as
static and dynamic analyses of deep underground mined openings. Another
application is the study of the response of reinforced concrete. The breaking of bonds
between blocks could simulate the progressive failure with crack propagation and
spalling.
A potential application area of UDEC is in studies related to earthquake engineering.
For example, the program may be used to explain some phenomena, like fault
movement.
4.6.3 Comparison with other methods
1) Differentiation
A general question is asked about UDEC: ‘Is UDEC a distinct element or a discrete
element program?’
The term ‘discrete element method’ applies to a computer program when it: (a) could
allow finite displacements and rotations of discrete bodies, even complete
detachment; and (b) could recognise new contacts automatically in progress.
The name ‘distinct element method’ refers to a particular discrete element scheme.
Distinct Element Programs use deformable contacts and an explicit, time-domain
solution of the equations of motion directly; bodies may be rigid or deformable by
subdivision into elements. UDEC falls in this category (UDEC Manual, 2005).
181
2) Characteristics
In order to simulate the behaviour of a discontinuous medium, many finite elements,
boundary elements and Lagrangian finite difference programs have developed
interface elements or slide lines to a limited extent only. For instance, their
formulation is usually restricted to small displacements and rotation; the logic may
break down when many intersecting interfaces are used. That is to say, the above
programs are more suited to dealing with continuum features rather than large
discontinuous media; UDEC is ideally suited to the study of potential modes of
failure directly related to the presence of discontinuous features.
4.6.4 General solution procedure
In this research, UDEC is used to simulate a set of physical models with hundreds of
discrete masonry bricks under static loading.
Firstly, to set up a model in UDEC, three fundamental components must be specified
as:
a) A distinct-element model block with cuts to create problem geometry;
b) Constitutive behaviour and material properties;
c) Boundary and initial conditions.
After these conditions have been defined in UDEC, an alteration is then performed
(such as excavating material or changing material properties), and the resulting
response of the model is calculated.
182
The general solution procedure for static analysis with UDEC is illustrated in Figure
4.54. This procedure represents the sequence of processes that occurs in the physical
environment.
Figure 4.54 General solution procedure for static analysis (Itasca, 2005)
MODEL SETUP
1. Generate model block, cut block to create problem geometry
2. Define constitutive behaviour and material properties
3. Specify boundary and initial conditions
Step to equilibrium state
PERFORM ALTERATIONS
For example,
Excavate material
Change boundary conditions
1. Specify boundary and initial
Step to solution
Examine the model response
Examine the model response
REPEAT FOR ADDITIONAL ALTERATION
183
4.6.5 Further developments
Since UDEC is a two-dimensional program, the three-dimensional geometry of a
joint structure cannot be represented, except for special orientations.
In order to evaluate the importance of three-dimensional geometry on the response of
a system, a three-dimensional numerical program, such as the Itasca code 3DEC or
PFC3D
, is required.
4.7 Numerical modelling of physical models using UDEC
4.7.1 Materials and interface properties
The Mohr-Coulomb constitutive model is also employed for numerical modelling in
UDEC. Similar to FLAC modelling, most of the material properties are obtained in
the laboratory, as mentioned in Section 4.2 Programme of material testing.
In terms of interfaces, UDEC is specially designed to model interacting bodies and
would replace FLAC in terms of more complicated interface problems such as
brickwork block (including mortar) joints.
In particular, the interface has two essential factors of normal and shear stiffness
between two blocks, which may contact each other. Figure 4.55 illustrates the joint
model, in which two blocks are connected by shear and normal stiffness springs,
joint tensile strength, joint friction angle and joint cohesion (Goodman et al., 1968).
184
Figure 4.55 Interface model in the UDEC code (Idris et al. 2009)
The values of Jkn and Jks depend on the contact area ratio, the relevant properties of
the joint filling material and blocks and the roughness of the joint surface. There are
two ways to determine the value of Jkn and Jks.
1° Rule-of-thumb (see Section 4.5.1)
2° After CUR (1994)
Figure 4.56 Model using Micro-modelling strategy
With the assumption of stack bond and uniform stress distributions in both brick and
mortar, the components of the elastic stiffness matrix D read, (Lourenco, 1996; CUR,
1994),
………………….………………………………………. (4.9)
…………………………………………………………(4.10) )(
)(
GmGbhm
GbGmks
EmEbhm
EbEmkn
hm
hu
hm
185
Where Eu and Em are the Young’s moduli, Gu and Gm are the shear moduli,
respectively, for brick and mortar and hm is the actual thickness of the joint.
4.7.2 Model generation
Similar to the model generation using FLAC, the first step was to specify the shape
of the whole model using several pieces of block. The procedure continued to split
the initial blocks of brick-lined tunnels into smaller blocks with the purpose of
generating interfaces between individual bricks (the thin mortar between bricks was
simplified and combined with brick as a whole). The blocks were then made
deformable by creating finite-difference triangular zones in each block (see Figure
4.57).
Next, the same boundary conditions and gravity were set as those in FLAC. The
material properties were assigned for the blocks and interfaces: the soil properties
were in blue, whilst brick combined with mortar properties were in green, as shown
in Figure 4.57 and as prescribed in the Mohr-Coulomb model. After setting to an
equilibrium state, vertical loading was then added until failure occurred. Thus, the
boundary conditions of the initial physical model were changed.
186
Figure 4.57 UDEC model grids with boundary conditions
4.7.3 Parametric study
Parametric studies of different variables were conducted by UDEC to simulate the
evolution of the mechanical properties of the materials and interfaces used. The
variations of the different parameters are shown below.
1) Uniform load
Baseline numerical model (1:1:6)
The properties of brickwork and brickwork / soil joints listed in Table 4.20 are the
same as those in FLAC baseline model A (1:1:6), whilst brickwork block joint
properties are displayed at the end. The pressure versus crown displacement curve of
the baseline model is compared with the variations of properties in the parametric
study.
187
Table 4.20 Brickwork block (mix proportion 1:1:6), brickwork / soil and
brickwork block joint properties
*: Poisson’s ratio of the brickwork and the friction angle of the joint (Jφ) were
initially referring to Idris et al., 2008.
Parametric study
UDEC baseline A, models A1 - A4: Initially the friction angle of the brickwork
block was decreased to 50° and 52° in UDEC A1 and A2 separately. As we could
see from Figure 4.58, the reducing values of the friction show a gradual decrease in
the slope, which is closer to the experiment result. In UDEC A3, the cohesion was
dropped to 0.16 MPa, as in the FLAC modelling. Thus, the crown displacement was
similar to the experiment curve at the ultimate load. The values of joint normal and
shear stiffness were both calculated in two ways (see Section 4.7.1). The above
models used the first method, while UDEC A4 changed to the second method with
which the crown displacement increased at ultimate load. After study, UDEC A3
was determined to be the most appropriate model to simulate physical model test 1.
Brickwork block (1:1:6)
ρ (kg/m³) E (MPa) v c (MPa) φ Tr (MPa)
1732 384.33 0.2* 0.1845 55° 0.2437
Brickwork / soil joint
JKn1 (GPa/m) JKs1 (GPa/m) Jc1 (MPa) Jφ1 JTr1 (MPa)
112.97 112.97 0 25* 0
Brickwork block joints
JKn2 (GPa/m) JKs2 (GPa/m) Jc2 (MPa) Jφ2 JTr2 (MPa)
112.97 112.97 0.1521 25* 0.218
188
Figure 4.58 Physical model 1 vs. UDEC model A curves
Table 4.21 shows the values of the parametric study.
Table 4.21 Brickwork parametric study (1:1:6)
Baseline numerical model (1:2:9)
The properties listed in Table 4.22 were used for the UDEC baseline model B (1:2:9).
The crown displacement curve of the baseline model was compared with other
UDEC models in the parametric study.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
UDEC Baseline
UDEC 1
UDEC 2
UDEC 3
UDEC 4
E (MPa) v c (MPa) φ
JKs2
(GPa/m)
JKn2
(GPa/m) Jφ2
Baseline A 384.33 0.2 0.1845 55° 112.97 112.97 25°
UDEC A1 384.33 0.2 0.1845 50° 112.97 112.97 25°
UDEC A2 384.33 0.2 0.1845 52° 112.97 112.97 25°
UDEC A3 384.33 0.2 0.16 50° 112.97 112.97 25°
UDEC A4 384.33 0.2 0.16 50° 28.83 69.18 25°
Physical model test 1
UDEC Baseline A
UDEC A1
UDEC A2
UDEC A3
UDEC A4
189
Table 4.22 Brickwork block (mix proportion 1:2:9), brickwork / soil and
brickwork block joint properties
*: Poisson’s ratio of the brickwork and the friction angle of the joint (Jφ) were
initially with reference to Idris et al., 2008.
Parametric study
UDEC baseline B, models B1 - B3: Figure 4.59 clearly illustrates the influence of
brickwork cohesion as well as the stiffness of brickwork block joints, where UDEC
B2 with the increase of cohesion up to 0.1 MPa could best represent the
displacement curve of physical model test 2. The stiffness of the brickwork block
joints using method 2 in UDEC B3 did not show any difference compared to UDEC
B2 using method 1. Thus, UDEC B2 was considered as the appropriate model here.
All the values of parametric study are shown in Table 4.23.
Brickwork (1:2:9)
ρ (kg/m³) E (MPa) v c (MPa) φ Tr (MPa)
1672.5 218.67 0.2* 0.0389 52° 0.0968
Brickwork / soil joint
JKn1 (GPa/m) JKs1 (GPa/m) Jc1 (MPa) Jφ1 JTr1 (MPa)
64.28 64.28 0 25* 0
Brickwork block joints
JKn2 (GPa/m) JKs2 (GPa/m) Jc2 (MPa) Jφ2 JTr2 (MPa)
64.28 64.28 0.0449 25* 0.066
190
Figure 4.59 Physical model 2 vs. UDEC model B curves
Table 4.23 Brickwork block parametric study (1:2:9)
2) Concentrated load
Baseline numerical model (1:2:9)
Again, the properties listed in Table 4.22 were used for the UDEC baseline model C
(1:2:9) under concentrated load. The crown displacement curve of baseline model C
was compared with other UDEC models in the parametric study in the next part.
0
0.2
0.4
0.6
0.8
1
1.2
0 50
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
UDEC Baseline'
UDEC 1'
UDEC 2'
UDEC 3'
E (MPa) v c (MPa) φ
JKs1
(GPa/m)
JKn2
(GPa/m) Jφ2
Baseline B 218.67 0.2 0.0389 52° 64.28 64.28 25°
UDEC B1 218.67 0.2 0.07 (79.94%) 52° 64.28 64.28 25°
UDEC B2 218.67 0.2 0.1 (157.07%) 52° 64.28 64.28 25°
UDEC B3 218.67 0.2 0.1 52° 22.05 52.92 25°
Physical model test 2
UDEC Baseline B
UDEC B1
UDEC B2
UDEC B3
191
Parametric study
UDEC baseline C, models C1 - C3: The cohesion of the brickwork was increased to
approach the experiment curve, from 0.1 MPa to 0.3 MPa. The increase of the
cohesion to 0.3 MPa was finally satisfied, as can be seen from Figure 4.60.
UDEC models C4 - C6: In models C4 to C6, the joint stiffness, cohesion and tensile
strength were varied separately to find out their influence on the numerical
modelling, compared to model C2 with the same cohesion of brickwork. Figure 4.61
demonstrates that the joint cohesion would not have much effect on the brickwork
block behaviour, while both joint tensile strength and joint stiffness show remarkable
influences on brickwork behaviour. However, these models would not represent
physical model test 3.
UDEC model C7: Finally, model C7 with 0.1 MPa joint tensile strength and
brickwork block cohesion was compared to model C3 with 0.066 MPa joint tensile
strength. The increased joint tensile strength leads to less stiffness of the crown
displacement curve shown in Figure 4.62.
In other words, The UDEC model C3 with 0.3 MPa cohesion was the best one to
represent physical model 3.
192
Table 4.24 Brickwork block parametric study (1:2:9) under concentrated load
Figure 4.60 Physical model 3 vs. UDEC baseline C & model C1 - C3 curves
0
0.2
0.4
0.6
0.8
0 10 20 30 40 50
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
UDEC Baseline''
UDEC 1''
UDEC 2''
UDEC 3''
E (MPa) c (MPa)
JKs1
(GPa/m)
JKn2
(GPa/m) Jc
JTr2
(MPa)
Baseline C 218.67 0.0389 64.28 64.28 0.0449 0.066
UDEC C1 218.67 0.1 64.28 64.28 0.0449 0.066
UDEC C2 218.67 0.2 64.28 64.28 0.0449 0.066
UDEC C3 218.67 0.3 64.28 64.28 0.0449 0.066
UDEC C4 218.67 0.2 64.28 64.28 0.1 0.066
UDEC C5 218.67 0.2 64.28 64.28 0.0449 0.1
UDEC C6 218.67 0.2 22.05 52.92 0.0449 0.066
UDEC C7 218.67 0.3 64.28 64.28 0.0449 0.1
Physical model test 3
UDEC Baseline C
UDEC C1
UDEC C2
UDEC C3
193
Figure 4.61 Physical model 3 vs. UDEC model C2 & C4 - C6 curves
Figure 4.62 Physical model 3 vs. UDEC model C3 & C7 curves
4.7.4 Results analysis of the parametric study
Parametric studies in the UDEC models have also been carried out in the last section
4.7.3; the discussions and comments are shown here.
0
0.2
0.4
0.6
0.8
0 10 20 30 40 50
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
UDEC 2''
UDEC 4''
UDEC 5''
UDEC 6''
0
0.2
0.4
0.6
0.8
0 10 20 30
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
UDEC 3''
UDEC 7''
Physical model test 3
UDEC C2
UDEC C4
UDEC C5
UDEC C6
Physical model test 3
UDEC C3
UDEC C7
194
1) The effect of strength properties
Brickwork block strength
As shown in Figure 4.58, for numerical models (1:1:6) the variation in the friction
angle of the brickwork blocks leads to large changes to the crown displacement
curve, whilst the decrease in the cohesion increases the crown displacement at failure.
This is closer to the physical model test result.
Brickwork block joint strength
In particular, the brickwork block joint strength parameters are studied for numerical
models under concentrated load in UDEC. The increase in brickwork block joint
cohesion only changes the crown displacement curve slightly. However, the increase
in joint tensile strength shows a large drop in the overall stiffness in Figure 4.61. The
reason may be that the stronger the joint tensile strength is, the more the tunnel
behaves like a continuum, leading to a shear failure at a lower load. The reduction in
the overall stiffness is also displayed in Figure 4.62 for the increase in joint tensile
strength (0.1 MPa) with increased brickwork block cohesion of 0.3 MPa.
2) The effect of stiffness properties
Brickwork block joint stiffness
Two calculation methods of joint stiffness with different values were used and input
into the numerical models. Under uniform load, the model with smaller values
slightly increases the crown displacement at the ultimate load. In contrast, the
reduction in joint stiffness shows a big change in the crown displacement curve for
the model under concentrated load. That is because the crown deforms much more
195
than other parts under concentrated load, where joint stiffness plays an important
role.
3) Comments
The UDEC modelling results imply that the cohesion of brickwork blocks seems to
be the predominant factor over others, followed by the friction angle of brickwork
blocks and, finally, joint tensile strength.
Neither joint cohesion or joint stiffness show a noticeable influence on the
mechanical behaviour of a brick-lined tunnel.
4.7.5 Modelling results
1) Uniform load
Numerical model (1:1:6)
The figures followed demonstrate the displacement and plastic state of the chosen
UDEC model A (UDEC A3) at certain loading level, simulating the results of
physical model test 1.
196
Figure 4.63 Displacement vectors of UDEC model A (1:1:6)
Figure 4.64 Plastic state of UDEC model A (1:1:6)
UDEC (Version 4.00)
LEGEND
18-Mar-13 21:03
cycle 28790
time = 1.817E+00 sec
displacement vectors
maximum = 2.859E-02
0 1E -1
boundary plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Displacement vectors (1:1:6)
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
UDEC (Version 4.00)
LEGEND
24-Mar-13 16:14
cycle 33350
time = 2.103E+00 sec
no. zones : total 1318
at yield surface (*) 130
yielded in past (X) 1016
tensile failure (o) 0
block plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic States (1:1:6)
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
197
Numerical model (1:2:9)
The displacement and plastic state of the chosen UDEC model B (UDEC B2) at
certain loading level were displayed in Figure 4.65 and Figure 4.66.
Figure 4.65 Displacement vectors of UDEC model B (1:2:9)
Figure 4.66 Plastic state of UDEC model B (1:2:9)
UDEC (Version 4.00)
LEGEND
24-Mar-13 20:32
cycle 11361
time = 7.684E-01 sec
displacement vectors
maximum = 2.801E-02
0 1E -1
boundary plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Displacement vectors (1:2:9)
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
UDEC (Version 4.00)
LEGEND
24-Mar-13 20:32
cycle 11361
time = 7.684E-01 sec
no. zones : total 1318
at yield surface (*) 94
yielded in past (X) 1031
tensile failure (o) 0
block plot
-0.200
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0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic States (1:2:9)
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
198
2) Concentrated load
Figure 4.67, Figure 4.68 and Figure 4.69 display the mechanical behaviour of the
UDEC model C (UDEC C3) at certain loading level (displacement vectors and
plastic state). In particular, tensile failure at the tunnel arch in Figure 4.68 shows a
good agreement with the experimental result, whilst failure pattern of the UDEC
model C in Figure 4.69 demonstrates the hinges and cracks at certain positions of the
tunnel arch.
Figure 4.67 Displacement vectors of UDEC model C (1:2:9) under concentrated
load
UDEC (Version 4.00)
LEGEND
26-Mar-13 22:20
cycle 15855
time = 1.054E+00 sec
displacement vectors
maximum = 1.311E-01
0 5E -1
boundary plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
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Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
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Figure 4.68 Plastic state of UDEC model C (1:2:9) under concentrated load
Figure 4.69 Failure pattern of UDEC model C (1:2:9) under concentrated load
showing hinges
UDEC (Version 4.00)
LEGEND
26-Mar-13 22:20
cycle 15855
time = 1.054E+00 sec
no. zones : total 1318
at yield surface (*) 538
yielded in past (X) 513
tensile failure (o) 82
block plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Concentrated load_Plastic States (1:2:9)
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
200
4.8 Discussion
4.8.1 Comparison with physical model tests
Numerical modelling results were analysed and compared with physical model tests
of brick-lined tunnels, as shown from Figure 4.70 to Figure 4.73.
The numerical modelling results have a good agreement with the mechanical
behaviour of the physical model tests in terms of both deformation characteristics
and failure pattern, thus proving that they could be effectively used in the study of
masonry tunnel stability.
These good agreements with physical model tests 1 - 3 encourage further predictions
of numerical modelling under various conditions, as discussed in the next section,
4.9.
Figure 4.70 Physical model test 1 vs. numerical curves
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 20 40 60 80
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 1
FLAC
UDEC
Physical model test 1
FLAC A
UDEC A
201
Figure 4.71 Physical model test 1 at 1/4 tunnel arch vs. numerical curves
Figure 4.72 Physical model test 2 vs. numerical curves
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Pre
ssu
re (
MP
a)
One quarter disp (mm)
Photogrammetry
FLAC
UDEC
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 2
FLAC'
UDEC'
Photogrammetry
FLAC A
UDEC A
Physical model test 2
FLAC B
UDEC B
202
Figure 4.73 Physical model test 3 vs. numerical curves
4.8.2 Comments
Notably, the value of brickwork cohesion of the FLAC numerical model was
normally smaller than the brickwork block cohesion in the UDEC model. The reason
might be that the brickwork in FLAC (containing mortar and the interface) should be
weaker than the brickwork block in UDEC (containing only mortar).
Taking the simulation of physical model 3 for an example, the FLAC numerical
model C used 0.2 MPa cohesion of brickwork that was about 5 times larger than the
laboratory result (0.0389 MPa), while in UDEC 0.3 MPa cohesion of brickwork
block was employed to match the physical model.
For the numerical models under uniform load that reached shear failure, the
mechanical behaviour of both the FLAC and UDEC models were very similar to
each other.
0
0.2
0.4
0.6
0.8
0 10 20 30
Pre
ssu
re (
MP
a)
Crown disp (mm)
Physical model test 3
FLAC''
UDEC''
Physical model test 3
FLAC C
UDEC C
203
For the numerical models under concentrated load, hinge failure occurred at the
ultimate load. UDEC modelling enabled the local and sophisticated mechanical
behaviour of discrete elements such as the cracking among brickwork blocks to be
shown.
In general, a micro-modelling strategy could give a better understanding of the local
failure behaviour of brickwork structures, whilst macro-modelling could simulate
deformation characteristics slightly better.
4.9 Prediction of numerical simulations
4.9.1 Introduction
Based on the proper numerical modelling, the deformation characteristics,
mechanical behaviour and probable failure mechanisms of the brick-lined tunnels
under different conditions are predicted by the combination of FLAC and UDEC
software.
In order to figure out the interaction of the overburden soil, brick-lined tunnel and
the soil depth effect on the tunnel, various soil depths (from the tunnel bottom) are
used in numerical modelling, from 980 mm to 1455 mm. 95 mm or 190 mm depth
may be added each time, as can be seen in Table 4.25.
Numerical models at different locations under concentrated load are then developed
to simulate the failure mechanism of ‘Brickwork Bridge’ under pavement.
204
Table 4.25 Prediction of numerical models under uniform and concentrated
load
4.9.2 Overburden soil depth
1) Uniform load test (1:1:6)
As can be seen in Figure 4.74, the increase in soil depth gradually decreases the
overall stiffness and failure load of the brick-lined tunnel. The shear failure not only
occurs at the tunnel sidewalls, but also extends to the tunnel arch as the soil depth
rises (see Appendix C).
Numerical
model No.
Overburden
soil depth (mm)
Depth
difference
(mm)
loading style Mortar mix
proportion
1 980
Uniform load 1:1:6 (higher
strength)
2 1075 95
3 1265 190
4 1455 190
7 980
Concentrated
load
1:2:9 (weaker
strength)
8 1075 95
9 1170 95
10 1265 95
205
Figure 4.74 Prediction of crown displacement curves under uniform load
2) Concentrated load test (1:2:9)
Figure 4.75 Prediction of crown displacement curves under concentrated load
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40 50 60 70
Pre
ssu
re (
MP
a)
Crown disp (mm)
FLAC P1_980mm
FLAC_Original_1075mm
FLAC P2_1265mm
FLAC P3_1455mm
0
0.2
0.4
0.6
0.8
0 10 20 30 40
Pre
ssu
re (
MP
a)
Crown disp (mm)
FLAC'' P1_980mm
FLAC''_Original_1075mm
FLAC'' P2_1170mm
FLAC'' P3_1265mm
206
Unlike the model under uniform load, an increase in the soil depth also increases the
overall stiffness of the brick-lined tunnel dramatically under concentrated load (see
Figure 4.75). Beyond a soil depth of 1265 mm, it is very hard to disperse the
concentrated load to the tunnel since most of the concentrated load would only be
dispersed to the soil below (see Appendix C).
4.9.3 Concentrated load
The performance of numerical modelling under concentrated load at different
positions is predicted as below, especially at one quarter across and at the middle of
the tunnel arch. The loading area is 0.1 m wide. UDEC modelling is used to predict
better local mechanical behaviour.
1) At one quarter across the tunnel arch
As an application of ‘Brickwork Bridge’ under pavement, Figure 4.76 demonstrates
the failure pattern and deformation of the UDEC model under concentrated load at
1/4 across the tunnel.
2) At the middle of the tunnel arch
Compared to the concentrated load at one quarter across the arch, where some part of
the load has been transferred to one side of the tunnel, the failure load at the middle
of the arch is smaller due to the direct tensile failure at the crown (see Figure 4.77).
207
Figure 4.76 Prediction of plastic state under concentrated load at 1/4 of the arch
Figure 4.77 Prediction of plastic state under concentrated load at 1/2 of the arch
UDEC (Version 4.00)
LEGEND
2-Apr-13 21:13
cycle 16875
time = 1.117E+00 sec
no. zones : total 1318
at yield surface (*) 349
yielded in past (X) 647
tensile failure (o) 34
block plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1/4
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
UDEC (Version 4.00)
LEGEND
2-Apr-13 21:09
cycle 20799
time = 1.383E+00 sec
no. zones : total 1318
at yield surface (*) 379
yielded in past (X) 617
tensile failure (o) 46
block plot
-0.200
0.200
0.600
1.000
1.400
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1/2
Itasca Consulting Group, Inc.
Minneapolis, Minnesota USA
208
4.10 Chapter summary
4.10.1 Programme of material testing
A series of laboratory material tests have been conducted as a major reference to the
numerical modelling work that followed, including brick, mortar, soil and their
interface properties.
4.10.2 FLAC and UDEC models
In order to analyse the mechanical behaviour of the brick-lined tunnels, numerical
models of physical model tests were developed with both the finite difference
method (in FLAC software) and the distinct element method (in UDEC software)
respectively. Their numerical results were then compared with the physical model
test data, giving reasonable results as well as revealing drawbacks.
4.10.3 Prediction of numerical modelling
After validation by physical model tests, the numerical simulation has developed and
predicted models at various soil depths under uniform load to show the interaction
between a brick-lined tunnel and the overburden soil at different locations under
concentrated load as a link to the engineering application of a ‘Brickwork Bridge’
under the pavement.
209
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions
The aim of this PhD research was to develop a numerical approach for a series of
small-scale physical models under extreme loading, using finite difference method
(FLAC software) and distinct element method (UDEC software) separately. The
stability of brick-lined tunnels has been assessed through both physical test models
and numerical models in this thesis. The research combines experimental,
monitoring and numerical modelling works together.
A comprehensive literature review has been carried out, concentrating on stability
issues of tunnels, tunnel monitoring methods, previous masonry structure research
and various numerical simulation approaches. Based on the literature review and
new laboratory tests of materials, the database of material properties (e.g. bricks,
mortar, surrounding soil and brickwork) corresponding to this research have been
built.
There were three small-scale physical tunnel models being designed and tested,
varying the mortar mix proportions. The mortar mix proportions were from
comparatively higher strength mortar mix comprising cement, lime and sand in
respective proportions of ratio 1:1:6 in the first physical tunnel model, to a mortar
mix proportion of lower strength (1:2:9) in the other two physical models. In
addition, the first and second physical tunnel models were under static uniform load
to simulate deep seated tunnels while the third model was under concentrated load to
simulate shallow tunnels subjected to traffic load.
210
Numerical modelling of three physical model tests was then carried out with the help
of the database of material properties, validated by the physical model results.
Parametric studies on the effects of stiffness properties and strength properties (e.g.
the Poisson’s ratio, Young’s modulus, friction angle and cohesion of the brickwork,
brickwork / soil interface stiffness and brickwork / soil joint friction angle) have
been conducted in the numerical models.
According to the physical model test results presented in Chapter 3, the following
conclusions can be drawn:
a) The physical tunnel model tests clearly indicated the mechanical behaviour of the
brick-lined tunnels under both uniform and concentrated loads until failure.
b) The failure pattern of physical models under uniform and concentrated load
differed. The first two physical models, which were under uniform load, failed as
a result of shear failure at the sidewalls as the major force was transferred to the
sides. The third physical model, which was under concentrated load, failed due to
the formation of five structural hinges at the tunnel arch.
c) The ultimate load capacity and mode of failure were also determined and
compared with different models. For both the first and the second physical
models under uniform load, built with different mortar mix proportions of the
brick-lined tunnels, ultimate capacity was affected by the compressive strength
of the tunnel materials.
d) The comparatively higher compressive strength of the brickwork in the first
physical model resulted in a higher ultimate load capacity than that of the second
physical model. It suggests a correlation between compressive strength of
constituent brickwork and ultimate load capacities of the tunnels. That the tunnel
211
comprising brickwork of higher strength failed later than its counterpart when
both were subject to identical load regimes.
e) The third physical model under concentrated load reduced the ultimate capacity
of the tunnel by approximately 30%, comparing with the model under uniform
load. A significant reason for the lower ultimate capacity of the third tunnel
model is due to uniaxial point loading. Comparatively, the first two physical
models under uniform load were subjected to the confining pressure from the
surrounding soil especially at sidewalls, which increased the ultimate capacity of
the brick-lined tunnels.
According to the tunnel monitoring results presented in Chapter 3, some conclusions
are drawn below:
f) Potentiometers were used to monitor tunnel deformation during the physical
model loading tests, providing a reference for tunnel monitoring work. In
addition, two advanced techniques photogrammetry and a laser scanning
system were employed to carry out monitoring tunnel deformation and
inspecting brickwork defects during the physical model loading tests.
g) Both advanced techniques are suitable for measuring tunnel defects, such as
major cracks on tunnel shells of around 3 to 5 mm wide. The accuracy of the
laser scanning technique is within 1.3 mm when compared with the vernier
calliper, while the accuracy of photogrammetry is within 1.0 mm.
h) Photogrammetry usually works with the help of daylight, or a lighting system in
a dark environment, whereas the laser scanning system performs well without
any aid of lighting to observe cracks and defects.
212
i) Photogrammetry shows a strong potential for measuring tunnel deformation with
high accuracy with the help of lighting. The centre point of target points can be
easily captured by Centroiding function in the related post-processing software
Australis, rather than ambiguous point cloud of the target points in the laser
scanning system.
According to the numerical modelling results presented in Chapter 4, some
conclusions are drawn as follows:
j) The numerical models have been built and validated by the three physical model
tests. The numerical modelling results have a good agreement with the
mechanical behaviour of the physical model tests in terms of both deformation
characteristics and failure pattern, thus proving that they could be effectively
used in the study of the stability of masonry tunnels.
k) The value of the brickwork cohesion of the FLAC numerical model was smaller
than the brickwork block cohesion in the UDEC model. The reason may be that
the brickwork in FLAC (containing mortar and the interface) should be weaker
than the brickwork block in UDEC (containing only mortar).
l) For the numerical models under uniform load that reached shear failure, the
mechanical behaviour of both the FLAC and UDEC models were very similar to
each other.
m) Generally, the micro-modelling strategy (used in UDEC) shows a better
agreement with the physical model test of the local failure behaviour of
brickwork structures. The failure pattern of the UDEC model under concentrated
load clearly demonstrates the hinges and cracks at certain positions of the tunnel
arch.
213
n) In another way, the macro-modelling strategy (applied in FLAC) reasonably
simulates the deformation characteristics and shows a good agreement with the
three physical model tests.
o) Results from the analysis confirmed that, in both numerical methods, the
cohesion of brickwork (blocks in UDEC) was the predominant factor, followed
by the friction angle of brickwork. These results agreed with the findings of Idris
et al. (2008). However, numerical models were not very sensitive to the
Poisson’s ratio, Young’s modulus of the brickwork, joint stiffness, joint cohesion
or the joint friction angle.
p) Prediction of numerical models at various soil depths under uniform load was to
show the interaction between a brick-lined tunnel and the overburdened soil;
prediction at different locations under concentrated load was linked to the
engineering application of a ‘Brickwork Bridge’ under the pavement. It was
shown that, under uniform load, shear failure not only occurred at the tunnel
sidewalls, but also extended to the tunnel arch. As the soil depth increased, the
concentrated load at the middle of the arch failed easily due to direct tensile
failure at the crown, compared to the load one quarter across the arch.
5.2 Recommendations for future research
Although the research work presented in this thesis has attempted to enhance the
understanding of the mechanical behaviour of brick-lined tunnels subjected to
uniform and concentrated loading conditions, several studies are recommended for
further investigation.
214
In further research, old tunnel structures, such as weathered or deteriorated
brickwork from the field, could be tested to obtain specific properties and these
could be input into numerical models.
As a recommendation for further modelling work, it is worth trying to introduce
other constitutive models related to masonry structures and simulate the longer term
deformation and stress conditions of brick-lined tunnels after years of degradation.
More realistic conditions could be applied, such as tunnels surrounded by anisotropic
geotechnical materials and cyclic loading, representing moving vehicles on the road.
In addition, 3D modelling using FLAC3D
and 3DEC could be used to develop a
better understanding of the actual interaction of bricks and mortar, and of the
mechanical behaviour of brick-lined tunnels.
It would also be possible to study mobile monitoring techniques combined with
Global Position System (GPS) in order to increase the efficiency of the investigation.
215
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IMAGING RESOURCE, Ltd.. (2009) From: http://www.imaging-
resource.com/PRODS/E5D2/E5D2A.HTM.
LEICA GEOSYSTEMS, Ltd. (2009) From: http://www.leica-
geosystems.com/downloads123/zz/tps/tps1200/brochures/Leica_TPS1200+_broc
hure_en.pdf.
PHOTOMETRIX (2007) User Manual for Australis, Version 7.0. Australia.
PLASSER AMERICAN Ltd. (2010) From:
http://www.plasseramerican.com/en/p_recording/ncms.htm.
http://www.plasseramerican.com/en/p_recording/messfahrzeuge.htm.
WIKIPEDIA (2013) From: http://en.wikipedia.org/wiki/Marc_Isambard_Brunel.
222
APPENDIX A LABORATORY TEST RESULTS
Table A.1 UCS test list of different mortar samples
Mortar Mix Proportion 1:2:9
Sample Average Average Sample Failure Ultimate Young’s
Reference Length Diameter Density Load Compressive Modulus
Strength
(mm) (mm) (g/cm3) (kN) (MPa) (GPa)
Sample 01 73.95 37.43 1.61 3.1 2.86 0.21
Sample 02 73.85 37.69 1.61 3.3 3.04 0.25
Sample 03 74.00 37.60 1.63 3.5 3.25 0.30
Average 73.93 37.57 1.62 3.3 3.05 0.25
Standard 0.08 0.13 0.01 0.20 0.20 0.044
Deviation
Mortar Mix Proportion 1:1:6
Sample Average Average Sample Failure Ultimate Young’s
Reference Length Height Density Load Compressive Modulus
Strength
(mm) (mm) (g/cm3) (kN) (MPa) (GPa)
Sample 01 74.17 37.50 1.67 5.1 4.73 0.39
Sample 02 73.86 37.76 1.62 4.6 4.26 0.31
Sample 03 73.88 37.60 1.64 4.6 4.25 0.29
Average 73.97 37.62 1.64 4.8 4.41 0.33
Standard 0.17 0.13 0.03 0.27 0.27 0.052
Deviation
223
Figure A.1 Load versus displacement curve of mortar mix 1:2:9
Figure A.2 Load versus displacement curve of mortar mix 1:1:6
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5
Lo
ad
(k
N)
Displacement (mm)
Uni-Axial Compressive Strength Test
Sample 1
Sample 2
Sample 3
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1 1.2
Load
(k
N)
Displacement (mm)
Uni-Axial Compressive Strength Test
Sample 1
Sample 2
Sample 3
224
Table A.2 UCS test list of brickwork triplets
Brickwork with Mortar Mix Proportion 1:2:9
Sample Average Average Average Sample Failure Ultimate Young’s
Reference Length Height Width Density Load Compressive Modulus
Strength
(mm) (mm) (mm) (g/cm3) (kN) (MPa) (GPa)
Sample 01 99 104 49 1.7631 29.94 6.18 0.233
Sample 02 98.5 105 49 1.7325 34.66 7.19 0.211
Sample 03 100 108 49.5 1.7022 35.25 7.13 0.212
Average 99.1667 105.667 49.1667 1.7326 33.2833 6.83333 0.21867
Standard 0.76376 2.08167 0.28868 0.03045 2.9104 0.5666 0.01242
Deviation
Brickwork with Mortar Mix Proportion 1:1:6
Sample Average Average Average Sample Failure Ultimate Young’s
Reference Length Height Width Density Load Compressive Modulus
Strength
(mm) (mm) (mm) (g/cm3) (kN) (MPa) (GPa)
Sample 01 102 109 48 1.6981 43.01 8.79 0.351
Sample 02 108 105 48 1.6803 37.62 7.26 0.249
Sample 03 102 109 49 1.6434 37.26 7.46 0.553
Average 104 107.667 48.3333 1.6739 39.2967 7.8367 0.38433
Standard 3.4641 2.3094 0.57735 0.02789 3.22087 0.83164 0.15472
Deviation
225
Figure A.3 Load versus displacement curve (brickwork triplet within mortar
mix proportion 1:2:9)
Figure A.4 Load versus displacement curve (brickwork triplet within mortar
mix proportion 1:1:6)
0
5000
10000
15000
20000
25000
30000
35000
40000
0 1 2 3 4 5 6 7
Lo
ad
(N
)
Displacement (mm)
Uni-Axial Compressive Strength Test
(Mortar mix proportion 1:2:9)
Test 1
Test 2
Test 3
0
10000
20000
30000
40000
50000
0 1 2 3 4
Load
(N
)
Displacement (mm)
Uni-Axial Compressive Strength Test (Mortar mix
proportion 1:1:6)
Test 1
Test 2
Test 3
226
Table A.3 The tensile strength test list of brickwork triplets
Mortar Mix Proportion 1:2:9
Sample Average Average Tensile Tensile
Reference Length Width Failure Strength
Load
(mm) (mm) (N) (MPa)
Sample 01 103.3 48.3 413.385 0.0829
Sample 02 103.9 41.4 282.297 0.0656
Sample 03 104.2 47.7 705.588 0.1420
Average 103.8 45.8 467.09 0.0968
Standard 0.45826 3.8223 216.696 0.0400
Deviation
Mortar Mix Proportion 1:1:6
Sample Average Average Tensile Tensile
Reference Length Width Failure Strength
Load
(mm) (mm) (N) (MPa)
Sample 01 99.6 50 1455.38 0.2922
Sample 02 99.5 50.2 1104.35 0.2211
Sample 03 102 50.9 1130.43 0.2177
Average 100.367 50.3667 1230.05 0.2437
Standard 1.41539 0.47258 195.576 0.0421
Deviation
227
Figure A.5 Tensile load versus extension curve (brickwork triplet within mortar
mix proportion 1:2:9)
Figure A.6 Tensile load versus extension curve (brickwork triplet within mortar
mix proportion 1:1:6)
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4 0.5 0.6
Ten
sile
Lo
ad
(N
)
Extension (mm)
Tensile Bond Strength Test
(Mortar mix proportion 1:2:9)
Test 1
Test 2
Test 3
0
200
400
600
800
1000
1200
1400
1600
0 0.2 0.4 0.6 0.8 1
Ten
sile
Load
(N
)
Extension (mm)
Tensile Bond Strength Test
(Mortar mix proportion 1:1:6)
Test 1
Test 2
Test 3
228
Table A.4 The shear strength test list of brickwork triplets
Mortar Mix Proportion 1:2:9
Sample Average Average Pre-compressive Failure Ultimate
Reference Length Width Stress Load Shear
Strength
(mm) (mm) (MPa) (kN) (MPa)
Sample 01 99.00 48.30 0.002 0.48 0.05
Sample 02 99.70 51.50 0.002 0.33 0.03
Sample 03 99.20 51.50 0.002 0.70 0.07
Sample 04 97.50 51.00 0.006 0.54 0.05
Sample 05 98.40 49.90 0.006 0.47 0.05
Sample 06 98.25 50.06 0.006 0.70 0.07
Sample 07 98.20 48.80 0.010 0.72 0.08
Sample 08 98.00 49.00 0.010 0.77 0.08
Sample 09 98.70 51.10 0.010 0.52 0.05
Average 98.55 50.13 - - -
Standard 0.67 1.22 - - -
Deviation
Mortar Mix Proportion 1:1:6
Sample Average Average Pre-compressive Failure Ultimate
Reference Length Width Stress Load Shear
Strength
(mm) (mm) (MPa) (kN) (MPa)
Sample 01 99.20 50.20 0.002 1.73 0.17
Sample 02 98.90 51.00 0.002 1.64 0.16
Sample 03 99.70 50.80 0.002 2.39 0.24
Sample 04 98.80 50.70 0.006 1.60 0.16
Sample 05 98.24 49.98 0.006 1.44 0.15
Sample 06 98.00 50.00 0.006 1.87 0.19
Sample 07 98.30 50.88 0.010 2.45 0.24
Sample 08 101.00 49.30 0.010 2.23 0.22
Sample 09 99.00 51.00 0.010 2.06 0.20
Average 99.02 50.43 - - -
Standard 0.91 0.59 - - -
Deviation
229
Figure A.7 Shear load versus displacement curve (brickwork triplet within
mortar mix proportion 1:2:9)
Figure A.8 Shear load versus displacement curve (brickwork triplet within
mortar mix proportion 1:1:6)
0
200
400
600
800
1000
0 0.2 0.4 0.6 0.8 1 1.2
Sh
ear
loa
d (
N)
Shear displacement (mm)
Shear Strength Test
(Mortar mix proportion 1:2:9)
Test 1_10N
Test 2_10N
Test 3_10N
Test 4_30N
Test 5_30N
Test 6_30N
Test 7_50N
Test 8_50N
0
500
1000
1500
2000
2500
3000
0 0.5 1 1.5
Sh
ear
load
(N
)
Shear displacement (mm)
Shear Strength Test
(Mortar mix proportion 1:1:6)
Test 1_10N
Test 2_10N
Test 3_10N
Test 4_30N
Test 5_30N
Test 6_30N
Test 7_50N
Test 8_50N
230
Figure A.9 Shear stress against precompression of brickwork triplet (1:2:9)
Figure A.10 Shear stress against precompression stress of brickwork triplet
(1:1:6)
0
0.02
0.04
0.06
0.08
0.1
0 0.005 0.01 0.015
Sh
ear
stre
ss (
MP
a)
Precompression stress (MPa)
Shear Strength Test
(Mortar mix proportion 1:2:9)
Test 1_10N
Test 2_10N
Test 3_10N
Test 4_30N
Test 5_30N
Test 6_30N
Test 7_50N
Test 8_50N
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.005 0.01
Sh
ear
stre
ss (
MP
a)
Precompression stress (MPa)
Shear Strength Test
(Mortar mix proportion 1:1:6)
Test 1_10N
Test 2_10N
Test 3_10N
Test 4_30N
Test 5_30N
Test 6_30N
Test 7_50N
Test 9_50N
Test 8_50N
231
APPENDIX B POST-PROCESSING WORK OF
MONITORING
5_6
6_7
232
7_8
8_9
233
9_10
10_11
234
11_12
12_13
235
13_14
14_15
236
15_16
16_17
237
17_18
18_19
238
19_20
20_21
239
APPENDIX C NUMERICAL MODELLING RESULTS OF
PREDICTION
Figure C.1 Plastic state of FLAC model (1:1:6) under uniform load at 980 mm
soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:07
step 38829
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 980mm soil depth
240
Figure C.2 Plastic state of FLAC model (1:1:6) under uniform load at 1265 mm
soil depth
Figure C.3 Plastic state of FLAC model (1:1:6) under uniform load at 1455 mm
soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:08
step 27527
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1265mm soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:08
step 24853
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1455mm soil depth
241
Figure C.4 Plastic state of FLAC model (1:2:9) under concentrated load at 980
mm soil depth
Figure C.5 Plastic state of FLAC model (1:2:9) under concentrated load at 1170
mm soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:09
step 123882
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
At Yield in Tension
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 980mm soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:17
step 115746
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1170mm soil depth
242
Figure C.6 Plastic state of FLAC model (1:2:9) under concentrated load at 1265
mm soil depth
FLAC (Version 6.00)
LEGEND
1-Apr-13 23:24
step 115340
-1.164E+00 <x< 1.164E+00
-4.839E-01 <y< 1.844E+00
state
Elastic
At Yield in Shear or Vol.
Elastic, Yield in Past
Grid plot
0 5E -1
-0.200
0.200
0.600
1.000
1.400
1.800
-0.800 -0.400 0.000 0.400 0.800
JOB TITLE : Plastic state at 1265mm soil depth